There’s way too much documentation about binary LFSRs out there, and not a whole lot on doing the same with other bases. Here are some tables for other bases so things can be thrown together without too much thought.

In the binary case one has a selection of taps which are either used or not used, and the next bit (digit) in the sequence is the parity of the taps one chose.

To extend this to base b, one can multiply each tap by an integer between 0 and b-1 (zero meaning the tap is unused), and add these up mod b, and that’s the next digit.

def nblfsr(punctured=True):
  base = 3
  poly = [0, 0, 0, 1, 2]
  shift = [1, 0, 0, 0, 0]

  while True:
    yield shift[0]
    x = sum(map(operator.mul, shift, poly)) % base
    shift = [x] + shift[:-1]
    if not punctured and x == 1 and not any(map(bool, shift[1:])):
      yield 0

Remembering the caveat that the all-zeroes pattern cannot occur in the sequence, a generator like this can produce a pseudorandom string in any alphabet with a period $b^n-1$. Such sequences are almost a de Bruijn sequence, where every possible length-n string is produced exactly once in the minimum number of steps possible.

I’ve also used it where I wanted a sequence where the new value is the previous value multiplied by 3, but with a small perturbation to ensure that after $b^n-1$ steps it wraps to follow a different path until all values (except for zero) are visited. This was as a team combination thing, in an arbitrary number of dimensions, or something like that, I think.

So here are some tables of viable polynomials in some other bases, just to help fill the gap. Not a comprehensive list but a quick scan yielding a few options from “sparse” to “dense” concentration of taps. Depending on the implementation one might want the lightest taps (fewest multiplies, fewest additions), or if those costs aren’t important then one might prefer the potentially more chaotic results from a denser mix.

Converting to a de Bruijn sequence

The one missing output sequence is the all-zeroes case. This seems to be known as a “punctured” de Bruijn sequence.

If we simply wait until the output is nearly all zeroes, and insert an extra zero, then we can fill that gap. And then to get back on track we need to recognise all-zeroes and output something other than another zero (which would be the natural consequence).

For base b there are b-1 cases where this run of n-1 zeroes case appears. Pick one (only one) of them, and insert the all-zeroes case in the sequence (ie., insert one more zero), and then carry on to what the next step would have been before the insertion; which will be the product of the last non-zero shifted out by the value of the last tap in the feedback polynomial.

It’s quite clumsy and not a thing I would want to bother with except that it might help with the following…

Extending to $p^n$ bases

If you need a generator with a base which is some power of a prime then you could use a prime generator which is n times longer and then combine groups of n digits into a single value.

However, one must be careful about the way sets of small values are mapped to larger values and the way the sequence is stepped. Either step the sequence in groups of n, so that the logical shift register structure is maintained, or use single steps and a more convoluted mapping which still looks like a shift register afterwards.

When stepping in ones there’s going to be some mathematical relationship between nearby values as a single value in the long shift register is going to move around and be re-used in the remapped shift register. This makes it a weaker PRNG.

When using steps greater than one care must be taken to ensure that the step is co-prime with the period of the generator. Only if it is co-prime can the shift register visit every possible state for a bijective mapping.

Otherwise, one would need to implement linear $\mathrm{GF}(p^n)$ arithmetic and either repeat the search, or find some polynomials using mathematics I haven’t learned. I haven’t got around to doing either of those things.

Also if I did the search I wolud then need to specify the multiplication and addition operations more explicitly because they’re not the same as for prime bases.

Extending to other bases

One can merge de Bruijn sequences of the same size but co-prime bases by effectively running them in parallel and splicing the outputs from sequences $u$ (base $b_u$) and $v$ (base $b_v$) as ${b_u}{x_v} + x_u$. The taps can either be drawn from separate shift registers for each base, or derived from the combined output using division and modulo by $b_u$.

What doesn’t work so well is trying to merge LFSR sequences this way. The trouble is that their periods are all in the form $p^n-1$, and that minus one makes it difficult to find coprime periods (all maximal non-binary periods are even).

Wikipedia links a reference for constructing de Bruijn sequences for arbitrary bases, but I’m not going to read all that.

Jumping around

Setting the de Bruijn modification aside because I don’t know how to account for that… you should be able to trivially construct a matrix representing the state change of the shift register (now a vector) to the next iteration. then just raise that matrix to the appropriate power (a series of squaring operations and conditional multiplications according to the bit pattern of the power) to get a matrix which will take you as far as you need to go.

Typically I like to have a solution handy for jumping ahead by the period of the generator times the golden ratio. You can use that to maximally distribute an arbitrary number of generators.

Example code

example code.

Tables

In the tables below, several different polynomials are listed for the given parameters, each enclosed in {}. The right-most value is the multiplier for the oldest output, and the leftmost value is the multiplier for the most recent output. The next result is:

\[x_{n+1} = \sum_{i=0}^{l-1} x_{n-i} p_i \mod b\]
base stages period polynomials
3 2 8 {1,1} {2,1}
3 3 26 {0,1,2} {1,2,2} {2,1,2}
3 4 80 {0,0,1,1} {1,1,2,1} {0,0,2,1}
3 5 242 {0,0,0,1,2} {0,0,1,2,2} {1,0,1,1,2} {1,2,2,2,2} {2,0,2,2,2}
3 6 728 {0,0,0,0,1,1}
{0,0,1,0,1,1} {1,1,0,2,0,1} {1,0,1,1,1,1} {1,1,1,1,1,1} {0,0,2,0,2,1} {0,2,0,1,2,1} {0,1,1,2,1,1} {1,2,2,1,2,1}
3 7 2186 {0,0,0,0,1,0,2}
{0,0,1,2,0,0,2} {0,0,0,1,1,1,2} {0,1,1,1,0,1,2} {0,1,1,1,1,2,2} {1,1,1,1,1,2,2} {0,0,0,0,2,1,2} {0,2,0,2,1,2,2} {0,1,1,1,2,2,2} {1,2,2,1,2,1,2}
3 8 6560 {0,0,0,0,1,0,0,1}
{0,0,0,1,1,0,2,1} {0,0,1,1,1,0,1,1} {0,0,1,1,1,1,1,1} {1,1,1,1,0,1,2,1} {1,1,1,1,1,1,2,1} {0,0,0,1,0,2,1,1} {0,0,0,2,1,2,2,1} {0,2,2,2,1,2,1,1} {1,1,1,2,2,2,2,1}
3 9 19682 {0,0,0,0,1,0,0,0,2}
{0,0,0,0,0,1,2,0,2} {0,0,0,0,0,1,1,1,2} {0,0,0,1,0,1,1,1,2} {0,0,1,1,0,1,1,2,2} {0,1,0,1,1,1,1,1,2} {0,1,1,1,1,1,1,1,2} {1,1,1,1,1,1,1,2,2} {0,0,0,0,1,2,1,2,2} {0,0,0,1,1,1,2,2,2} {0,0,1,2,2,2,1,2,2} {0,1,1,1,2,2,1,2,2} {1,2,1,1,1,2,2,2,2}
3 10 59048 {0,0,0,0,0,0,1,0,1,1}
{0,0,0,0,1,1,0,2,0,1} {0,0,0,0,1,0,1,1,1,1} {0,0,0,1,1,1,1,0,1,1} {0,0,0,1,1,1,1,1,2,1} {0,1,1,1,1,0,1,1,1,1} {1,1,1,0,1,1,1,1,1,1} {1,1,1,1,1,1,1,2,2,1} {0,0,0,0,0,1,0,2,1,1} {0,0,0,0,0,1,1,2,1,1} {0,0,0,0,1,2,2,1,2,1} {0,0,0,2,2,1,2,2,2,1} {0,0,2,1,1,1,1,1,1,1} {0,2,1,1,2,1,2,2,2,1} {2,1,2,1,2,2,1,2,1,1}
3 11 177146 {0,0,0,0,0,0,0,0,1,0,2}
{0,0,0,0,0,1,2,0,0,0,2} {0,0,0,0,0,0,1,0,1,1,2} {0,0,0,0,0,1,0,1,1,1,2} {0,0,0,0,1,1,1,1,2,0,2} {0,0,0,1,1,1,0,1,1,1,2} {0,0,1,1,0,1,1,1,1,1,2} {1,0,0,1,1,1,1,1,1,2,2} {0,1,1,1,1,1,1,1,1,1,2} {1,1,1,1,1,1,1,2,2,2,2} {0,0,0,0,0,0,2,0,2,2,2} {0,0,0,0,0,0,2,1,2,1,2} {0,0,0,0,0,1,2,2,2,2,2} {0,0,0,0,1,1,1,1,1,2,2} {0,0,0,1,1,1,2,2,1,2,2} {0,0,1,2,2,1,2,1,2,1,2} {0,1,2,1,2,1,1,1,2,2,2} {1,2,2,1,2,1,1,2,2,1,2}
3 12 531440 {0,0,0,0,0,0,1,0,0,0,1,1}
{0,0,0,0,0,0,1,1,0,0,2,1} {0,0,0,0,0,1,1,1,0,1,0,1} {0,0,0,0,0,1,1,1,0,1,1,1} {0,0,0,0,1,1,1,1,1,2,0,1} {0,0,0,1,1,0,1,1,1,1,1,1} {0,1,0,1,0,1,1,1,1,1,1,1} {0,0,1,1,1,1,1,1,1,1,2,1} {0,1,1,1,1,1,1,1,1,2,1,1} {1,1,1,1,1,1,1,2,1,1,2,1} {0,0,0,0,0,0,0,1,2,1,1,1} {0,0,0,0,0,1,0,2,1,1,2,1} {0,0,0,0,0,2,1,2,2,2,1,1} {0,0,0,0,1,1,1,1,2,1,1,1} {0,0,0,2,2,2,2,2,1,1,1,1} {0,0,1,1,2,2,2,2,2,2,2,1} {0,2,2,1,2,1,1,1,1,1,1,1} {1,1,1,2,2,1,2,1,1,2,2,1}
3 13 1594322 {0,0,0,0,0,0,0,0,0,0,0,1,2}
{0,0,0,0,0,0,0,0,0,1,2,0,2} {0,0,0,0,0,0,0,0,0,1,1,1,2} {0,0,0,0,0,0,1,0,1,0,1,1,2} {0,0,0,0,0,1,1,1,0,1,0,2,2} {0,0,0,0,0,1,1,1,0,1,1,1,2} {0,0,0,0,0,1,1,1,1,1,1,1,2} {0,0,1,0,1,1,1,0,1,1,1,2,2} {0,0,1,1,1,0,1,1,1,1,1,1,2} {0,1,0,1,1,1,1,1,1,1,1,1,2} {0,1,1,1,1,1,1,1,1,1,1,2,2} {1,1,1,1,1,1,1,1,1,2,2,2,2} {0,0,0,0,0,0,0,2,0,1,1,2,2} {0,0,0,0,0,0,1,0,1,2,2,1,2} {0,0,0,0,0,0,1,1,1,2,1,1,2} {0,0,0,0,0,2,2,1,1,2,2,2,2} {0,0,0,0,2,1,2,2,1,1,2,2,2} {0,0,0,1,2,1,2,2,2,1,2,2,2} {0,0,1,1,1,1,1,2,2,2,2,2,2} {0,1,1,1,2,2,2,2,1,1,1,2,2} {1,2,2,1,2,1,1,2,1,2,2,2,2}
3 14 4782968 {0,0,0,0,0,0,0,0,0,0,0,0,1,1}
{0,0,0,0,0,0,0,0,1,0,1,0,0,1} {0,0,0,0,0,0,0,0,0,1,1,2,0,1} {0,0,0,0,0,0,0,1,0,1,0,1,1,1} {0,0,0,0,0,0,0,1,0,1,1,1,1,1} {0,0,0,0,0,0,0,1,1,1,1,1,2,1} {0,0,0,0,0,1,1,1,0,1,1,1,1,1} {0,0,0,0,1,1,1,1,1,1,1,0,1,1} {0,0,0,1,1,1,1,0,1,1,1,1,2,1} {0,0,1,0,1,1,1,1,1,1,1,1,1,1} {0,1,1,1,0,1,1,1,1,1,1,1,1,1} {1,1,0,1,1,1,1,1,1,1,1,1,2,1} {1,1,1,1,1,1,1,1,1,1,1,1,1,1} {0,0,0,0,0,0,0,0,0,1,1,2,1,1} {0,0,0,0,0,0,0,0,2,1,1,2,2,1} {0,0,0,0,0,0,0,1,1,1,1,2,1,1} {0,0,0,0,0,0,1,1,1,1,2,1,1,1} {0,0,0,0,0,2,2,2,1,2,1,2,2,1} {0,0,0,0,1,1,2,2,1,1,2,2,1,1} {0,0,0,2,1,2,1,2,1,2,1,2,2,1} {0,0,1,1,1,2,2,1,2,1,1,2,2,1} {0,2,1,1,2,1,1,2,2,1,1,2,1,1} {2,2,2,2,2,2,1,2,2,2,2,1,1,1}
3 15 14348906 {0,0,0,0,0,0,0,0,0,0,0,0,1,0,2}
{0,0,0,0,0,0,0,0,0,0,0,0,1,2,2} {0,0,0,0,0,0,0,0,1,0,0,1,0,1,2} {0,0,0,0,0,0,0,1,0,0,0,1,1,1,2} {0,0,0,0,0,0,0,0,0,1,1,1,1,2,2} {0,0,0,0,0,0,1,0,1,0,1,1,1,1,2} {0,0,0,0,0,0,0,1,1,1,1,1,1,1,2} {0,0,0,0,1,0,1,1,0,1,1,1,1,2,2} {0,0,0,0,1,1,1,1,1,1,0,1,1,1,2} {0,0,0,1,1,1,1,1,1,1,1,1,0,1,2} {0,1,0,0,1,1,1,1,1,1,1,1,1,2,2} {0,1,0,1,1,1,1,1,1,1,1,1,1,1,2} {1,1,0,1,1,1,1,1,1,1,1,1,1,1,2} {1,1,1,1,1,1,1,1,1,1,2,1,1,1,2} {0,0,0,0,0,0,0,0,1,1,1,1,1,2,2} {0,0,0,0,0,0,0,1,1,1,2,2,1,2,2} {0,0,0,0,0,0,1,2,2,1,2,1,2,1,2} {0,0,0,0,0,1,1,2,2,2,1,1,2,1,2} {0,0,0,0,1,2,2,1,2,1,1,2,2,1,2} {0,0,0,1,1,1,1,1,2,2,2,2,1,1,2} {0,0,2,2,2,2,2,1,1,2,1,1,2,1,2} {0,1,2,2,1,2,1,1,2,1,2,2,2,2,2} {2,1,1,1,2,1,1,2,1,1,2,1,1,1,2}
3 16 43046720 {0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1}
{0,0,0,0,0,0,0,0,0,0,1,1,0,2,0,1} {0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1} {0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1} {0,0,0,0,0,0,0,0,1,1,0,1,1,1,2,1} {0,0,0,0,0,0,0,1,1,1,0,1,1,1,1,1} {0,0,0,0,0,1,0,1,0,1,1,1,1,1,1,1} {0,0,0,0,0,1,1,1,1,0,1,1,1,1,2,1} {0,0,0,1,0,1,1,1,0,1,1,1,1,1,1,1} {0,0,0,1,1,1,1,1,1,1,0,1,1,1,1,1} {0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,1} {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1} {1,1,1,1,1,0,1,1,1,1,1,1,1,2,2,1} {1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1} {0,0,0,0,0,0,0,0,0,1,2,1,1,1,1,1} {0,0,0,0,0,0,0,0,2,1,1,1,1,1,1,1} {0,0,0,0,0,0,0,2,2,2,2,2,1,1,1,1} {0,0,0,0,0,0,1,1,1,2,2,1,2,2,1,1} {0,0,0,0,0,2,1,2,2,2,1,1,1,2,2,1} {0,0,0,0,1,2,1,2,1,2,2,1,2,1,2,1} {0,0,0,1,1,1,2,2,1,2,1,1,2,2,1,1} {0,0,1,2,1,2,2,2,2,2,2,1,2,1,2,1} {0,2,2,2,1,1,2,2,1,2,1,1,2,2,2,1} {2,2,2,1,1,1,2,1,1,2,1,2,1,1,2,1}
3 17 129140162 {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2}
{0,0,0,0,0,0,0,0,0,0,0,1,2,0,0,0,2} {0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,1,2} {0,0,0,0,0,0,0,0,0,0,1,0,1,1,1,0,2} {0,0,0,0,0,0,0,0,0,0,1,1,1,1,2,0,2} {0,0,0,0,0,0,0,0,1,0,1,0,1,1,1,1,2} {0,0,0,0,0,0,0,0,1,1,1,1,0,1,1,1,2} {0,0,0,0,0,0,0,1,1,1,1,0,1,1,1,2,2} {0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,2} {0,0,0,0,1,1,0,1,0,1,1,1,1,1,1,1,2} {0,0,0,1,1,0,1,1,0,1,1,1,1,1,1,2,2} {0,0,1,0,1,0,1,1,1,1,1,1,1,1,1,1,2} {0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,2} {0,1,1,1,1,0,1,1,1,1,1,1,1,1,1,2,2} {1,1,1,1,0,1,1,1,1,1,1,1,1,1,1,1,2} {1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,2,2} {0,0,0,0,0,0,0,0,0,0,2,0,1,2,2,2,2} {0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,2,2} {0,0,0,0,0,0,0,0,0,1,1,2,2,1,1,1,2} {0,0,0,0,0,0,0,0,1,2,1,1,1,2,2,2,2} {0,0,0,0,0,0,0,2,1,1,1,1,1,2,1,2,2} {0,0,0,0,0,0,1,1,2,1,2,1,1,1,1,2,2} {0,0,0,0,0,2,1,2,2,1,2,1,1,2,2,2,2} {0,0,0,0,2,2,2,1,2,1,2,1,2,1,2,1,2} {0,0,0,1,1,1,1,1,2,2,2,2,1,2,2,1,2} {0,0,1,1,2,2,1,2,1,2,2,1,2,2,1,2,2} {0,2,2,2,2,1,2,1,2,1,1,1,1,1,1,1,2} {2,1,1,2,1,2,1,2,1,2,2,2,1,1,1,2,2}
3 18 387420488 {0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,0,0,1}
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{0,0,0,0,0,0,0,0,0,0,1,0,0,1,2} {0,0,0,0,0,0,0,0,0,0,1,1,1,0,2} {0,0,0,0,0,0,0,0,1,0,1,1,1,0,3} {0,0,0,0,0,0,1,0,0,1,1,0,1,1,2} {0,0,0,0,0,0,1,0,1,1,1,1,0,1,2} {0,0,0,0,0,0,1,1,1,1,1,0,1,1,2} {0,0,0,0,1,1,1,1,0,1,1,1,0,1,2} {0,0,0,1,0,0,1,1,1,1,1,1,1,1,3} {0,0,0,1,1,1,0,1,1,1,1,1,1,1,2} {0,0,1,1,1,1,0,1,1,1,1,1,1,1,2} {0,1,1,0,1,1,1,1,1,1,1,1,1,1,2} {1,1,1,1,0,1,1,1,1,1,1,1,1,1,2} {1,1,1,1,1,1,1,1,1,1,1,1,1,2,3} {0,0,0,0,0,0,0,0,0,1,4,2,1,4,2} {0,0,0,0,0,0,0,0,4,2,1,3,4,1,2} {0,0,0,0,0,0,0,2,2,4,1,2,1,3,3} {0,0,0,0,0,0,4,2,1,3,4,4,1,2,3} {0,0,0,0,0,1,1,4,2,1,3,4,4,2,2} {0,0,0,0,4,2,3,2,3,1,4,4,3,4,3} {0,0,0,2,3,1,1,3,4,1,4,2,4,2,3} {0,0,2,1,3,2,3,2,4,3,1,4,4,1,2} {0,3,1,4,1,3,3,3,3,1,1,4,2,2,2} {4,3,2,4,4,2,2,2,3,4,2,3,4,2,2}
7 2 48 {1,4}
7 3 342 {1,0,3} {1,1,3} {0,1,5} {4,6,3}
7 4 2400 {1,1,0,2} {1,1,2,2} {0,4,3,2} {1,2,2,4}
7 5 16806 {0,0,0,1,3}
{0,1,1,0,3} {0,1,1,1,3} {1,1,1,1,3} {0,0,4,6,3} {0,5,5,1,3} {1,5,6,4,5}
7 6 117648 {0,0,1,0,1,2}
{0,1,0,1,1,2} {0,1,1,1,1,2} {1,1,1,1,1,4} {0,0,0,1,4,2} {0,0,1,2,2,4} {0,1,3,2,3,2} {6,3,6,5,4,4}
7 7 823542 {0,0,0,0,0,1,3}
{0,0,0,1,1,0,3} {0,0,0,1,1,1,3} {0,1,0,1,1,1,3} {0,1,1,1,1,2,5} {1,1,1,1,1,2,5} {0,0,0,5,1,0,5} {0,0,0,1,6,6,3} {0,0,4,2,5,3,3} {0,6,5,4,3,5,3} {4,2,5,4,6,2,5}
7 8 5764800 {0,0,0,0,0,0,1,4}
{0,0,0,1,1,0,0,2} {0,1,0,0,1,1,0,2} {0,0,1,1,1,1,0,2} {0,1,1,0,1,1,1,4} {1,1,1,1,1,0,1,4} {1,1,1,1,1,1,1,4} {0,0,0,0,2,0,2,2} {0,0,0,0,3,5,1,2} {0,0,0,6,2,5,6,4} {0,0,6,3,6,5,4,4} {0,6,4,1,2,6,1,4} {4,4,3,6,1,2,3,4}
7 9 40353606 {0,0,0,0,0,0,1,0,3}
{0,0,0,0,1,0,0,1,3} {0,0,0,0,0,1,1,1,3} {0,0,0,1,0,1,1,1,3} {0,1,0,1,0,1,1,1,5} {0,1,1,1,1,0,1,1,3} {1,1,1,1,0,1,1,1,3} {1,1,1,1,1,1,1,1,5} {0,0,0,0,0,1,5,6,5} {0,0,0,0,1,6,3,5,5} {0,0,0,1,4,5,5,5,5} {0,0,3,1,3,1,6,4,3} {0,4,2,5,4,6,5,3,3} {3,4,4,4,5,6,5,1,3}
7 10 282475248 {0,0,0,0,1,0,1,0,0,2}
{0,0,0,1,1,0,0,1,0,2} {0,0,0,1,0,0,1,1,1,2} {0,0,1,0,1,0,1,1,1,2} {0,0,1,0,1,1,1,1,1,4} {1,0,1,0,1,1,1,1,1,2} {1,1,1,1,0,1,1,1,1,2} {1,1,1,1,1,1,1,1,3,2} {0,0,0,0,0,0,3,1,3,4} {0,0,0,0,0,4,6,6,5,4} {0,0,0,0,2,6,5,5,1,2} {0,0,0,1,6,4,2,4,3,4} {0,0,1,2,2,3,3,6,6,4} {0,3,5,1,3,3,6,2,1,4} {4,2,2,6,3,1,1,6,2,4}
7 11 1977326742 {0,0,0,0,0,1,0,1,0,0,3}
{0,0,0,0,0,0,0,1,1,1,3} {0,0,0,1,0,0,1,1,1,0,3} {0,0,0,0,1,1,1,1,0,1,5} {0,0,1,1,0,1,1,0,1,1,3} {0,0,1,1,0,1,1,1,1,1,3} {1,0,1,1,0,1,1,1,1,1,3} {1,1,1,0,1,1,1,1,1,1,3} {1,1,1,1,1,1,1,1,1,2,3} {0,0,0,0,0,0,0,3,2,3,5} {0,0,0,0,0,0,6,1,1,4,5} {0,0,0,0,0,1,6,6,6,3,5} {0,0,0,0,4,2,5,4,6,2,5} {0,0,0,5,5,2,4,6,1,5,3} {0,0,5,3,2,4,4,6,4,4,5} {0,6,3,4,4,5,3,2,3,1,3} {5,5,2,4,6,4,1,4,1,5,3}
7 12 13841287200 {0,0,1,0,0,0,0,1,0,0,0,2}
{0,0,0,0,1,1,0,1,0,0,0,2} {0,0,0,0,0,0,1,1,0,1,1,2} {0,0,0,1,0,1,0,1,1,0,1,2} {0,0,0,1,0,1,1,1,0,1,1,4} {0,0,0,1,1,1,1,1,1,1,0,2} {0,1,0,0,1,1,1,1,1,1,1,2} {0,1,1,1,1,1,1,1,0,1,1,2} {1,1,1,1,1,1,1,1,1,0,1,2} {1,1,1,1,1,1,1,1,1,4,5,2} {0,0,0,0,0,0,0,1,5,2,2,4} {0,0,0,0,0,0,2,6,5,5,1,2} {0,0,0,0,0,3,6,1,6,2,1,2} {0,0,0,0,1,6,4,3,1,6,5,2} {0,0,0,5,5,1,5,4,2,3,3,2} {0,0,1,6,4,3,2,6,1,5,3,4} {0,5,1,4,3,3,4,2,4,2,1,2} {3,5,1,3,3,6,2,4,6,1,3,2}
11 2 120 {1,3}
11 3 1330 {1,0,2} {1,1,6} {0,1,7} {3,7,6}
11 4 14640 {1,0,0,3} {1,0,1,9} {1,1,1,5} {0,0,1,9} {0,10,2,3} {2,3,1,3}
11 5 161050 {0,0,1,0,2}
{0,0,1,1,2} {0,1,1,1,2} {1,1,1,1,6} {0,3,0,0,6} {0,0,10,4,7} {0,5,5,9,2} {10,5,8,8,7}
11 6 1771560 {0,0,1,1,0,4}
{1,1,1,0,0,3} {1,1,1,0,3,4} {1,1,1,1,2,4} {0,0,0,10,2,3} {0,0,9,8,6,9} {0,8,7,3,4,4} {2,5,5,3,1,4}
11 7 19487170 {0,0,0,0,1,0,2}
{0,0,1,1,0,0,2} {0,1,0,1,1,0,2} {0,1,1,1,0,1,2} {1,1,0,1,1,1,6} {1,1,1,1,1,2,2} {0,0,0,0,10,4,7} {0,0,0,5,5,9,2} {0,0,1,3,1,7,2} {0,7,4,9,7,2,2} {4,10,2,5,2,10,8}
11 8 214358880 {0,0,0,1,1,0,0,3}
{1,0,1,0,0,1,0,3} {0,0,1,1,0,1,1,3} {0,1,1,1,0,1,1,5} {1,1,0,1,1,1,1,3} {1,1,1,1,1,1,1,3} {0,0,0,0,0,1,4,5} {0,0,0,0,9,6,4,5} {0,0,0,9,3,5,2,5} {0,0,10,3,6,3,5,9} {0,10,4,7,5,10,8,3} {2,5,5,3,1,8,8,4}
11 9 2357947690 {1,0,0,0,0,0,0,0,6}
{0,0,1,0,0,0,1,0,2} {0,0,0,0,1,1,1,0,2} {0,0,1,0,1,0,1,1,2} {0,0,1,1,1,1,0,1,2} {0,1,1,1,1,1,1,0,2} {1,1,1,0,1,1,1,1,2} {1,1,1,1,1,1,1,3,8} {0,0,0,0,0,1,6,10,2} {0,0,0,0,8,3,10,3,2} {0,0,0,2,9,4,7,4,7} {0,0,8,4,10,10,4,8,6} {0,2,9,10,8,9,6,1,8} {6,1,4,9,9,3,6,2,6}
11 10 25937424600 {0,0,0,0,0,0,1,1,0,3}
{0,0,0,0,0,1,1,1,0,3} {0,0,1,0,1,1,0,1,0,3} {0,0,0,1,1,1,1,1,0,3} {0,0,1,1,1,1,0,1,1,3} {1,1,1,0,1,1,1,1,0,3} {1,0,1,1,1,1,1,1,1,9} {1,1,1,1,1,1,1,1,1,4} {0,0,0,0,0,0,5,9,7,9} {0,0,0,0,0,5,5,3,3,5} {0,0,0,0,3,1,7,1,1,5} {0,0,0,5,6,4,3,3,3,9} {0,0,3,1,7,1,2,2,1,5} {0,3,10,7,2,9,1,9,6,5} {1,8,2,3,6,9,10,2,8,9}
13 2 168 {1,11}
13 3 2196 {1,0,2} {1,1,7} {2,0,2} {5,12,2}
13 4 28560 {1,1,0,2} {1,1,3,2} {0,4,2,11} {1,3,6,6}
13 5 371292 {1,0,1,0,2}
{1,1,1,0,2} {1,1,1,2,6} {4,0,0,0,11} {0,0,4,2,11} {0,8,7,7,6} {3,9,2,5,2}
13 6 4826808 {0,0,1,1,0,2}
{1,1,0,1,0,2} {1,0,1,1,1,2} {1,1,1,1,1,6} {0,0,0,1,3,6} {0,0,1,6,4,2} {0,7,7,7,12,2} {9,8,3,6,6,7}
13 7 62748516 {0,0,1,0,0,0,2}
{0,1,0,1,0,0,2} {0,0,0,1,1,1,2} {0,1,1,1,1,0,2} {0,1,1,1,1,1,2} {1,1,1,1,1,1,6} {0,0,0,0,8,4,6} {0,0,0,6,2,3,2} {0,0,6,2,10,1,6} {0,1,10,11,8,11,11} {1,12,2,7,5,2,6}
13 8 815730720 {0,0,0,1,0,0,1,2}
{0,0,1,0,1,0,1,2} {0,1,1,1,0,1,0,2} {1,1,0,1,0,1,1,6} {1,0,1,1,1,1,1,6} {1,1,1,1,1,1,4,2} {0,0,0,0,0,4,2,11} {0,0,0,0,8,7,7,6} {0,0,0,11,2,1,6,2} {0,0,8,12,10,6,7,6} {0,7,2,7,7,10,7,7} {4,4,7,8,10,8,2,11}
13 9 10604499372 {0,0,0,0,1,0,0,0,6}
{0,0,0,0,0,1,0,1,2} {0,0,0,0,0,1,1,1,2} {0,0,0,0,1,1,1,1,2} {0,0,1,1,1,1,1,0,2} {0,1,1,1,1,0,1,1,2} {1,1,1,1,1,1,1,0,2} {1,1,1,1,1,1,1,2,2} {0,0,0,0,0,1,10,10,7} {0,0,0,0,11,2,1,6,2} {0,0,0,9,8,3,6,6,7} {0,0,3,9,2,8,10,11,6} {0,6,2,10,8,9,3,12,2} {4,4,7,8,10,8,5,6,11}
17 2 288 {1,7}
17 3 4912 {0,1,3} {1,1,3} {2,15,5}
17 4 83520 {0,0,1,6} {1,0,1,10} {1,1,2,10} {0,5,12,10} {11,12,4,14}
17 5 1419856 {0,1,0,0,3}
{1,0,0,1,3} {1,0,1,1,3} {1,1,1,1,7} {0,0,0,1,6} {0,0,4,1,7} {0,6,3,6,5} {4,15,10,15,3}
17 6 24137568 {0,0,0,0,1,5}
{1,0,0,0,1,5} {0,0,1,1,1,6} {0,1,1,1,1,10} {1,1,1,1,2,10} {0,0,0,12,9,6} {0,0,7,9,11,5} {0,9,4,14,4,10} {6,3,7,8,6,10}
17 7 410338672 {0,0,0,0,0,1,3}
{0,0,1,0,0,1,3} {0,1,0,0,1,1,3} {0,1,1,1,0,1,3} {0,1,1,1,1,1,3} {1,1,1,1,1,1,3} {0,0,0,0,8,7,11} {0,0,0,16,1,7,5} {0,0,1,14,3,15,14} {0,4,5,12,14,1,7} {7,8,5,9,10,1,11}
17 8 6975757440 {0,0,1,0,0,0,0,7}
{0,0,0,1,1,0,0,3} {0,0,0,1,1,1,0,3} {0,0,1,1,1,1,0,3} {0,1,1,1,1,0,1,3} {1,1,1,1,0,1,1,3} {1,1,1,1,1,1,2,5} {0,0,0,0,0,14,11,6} {0,0,0,0,4,15,10,3} {0,0,0,1,14,3,15,14} {0,0,1,14,3,16,5,3} {0,3,1,16,7,4,8,10} {15,7,12,12,10,1,9,14}
17 9 118587876496 {0,0,0,0,0,0,1,0,3}
{0,0,0,0,1,0,0,1,3} {0,0,0,1,0,1,1,0,3} {0,0,1,1,0,1,0,1,3} {0,1,0,1,1,0,1,1,3} {1,0,0,1,1,1,1,1,3} {1,1,1,1,1,1,1,0,5} {1,1,1,1,1,1,1,1,7} {0,0,0,0,0,4,15,10,3} {0,0,0,0,3,12,15,8,11} {0,0,0,13,10,2,1,11,6} {0,0,1,4,5,12,14,3,7} {0,12,7,7,5,6,16,8,3} {11,12,7,7,13,4,14,6,3}
19 2 360 {1,5}
19 3 6858 {1,0,3} {1,1,10} {0,1,15} {1,15,15}
19 4 130320 {1,0,0,4} {0,1,1,4} {1,1,1,9} {3,0,0,5} {0,2,8,16} {2,7,5,9}
19 5 2476098 {1,0,0,0,2}
{0,1,0,1,2} {0,1,1,1,2} {1,1,1,1,10} {0,0,0,1,3} {0,0,1,4,14} {0,1,15,15,15} {13,11,4,5,10}
19 6 47045880 {1,0,0,0,0,4}
{0,0,1,1,0,5} {0,1,1,0,1,4} {1,1,0,1,1,5} {1,1,1,1,2,5} {0,0,0,18,8,6} {0,0,3,2,1,17} {0,6,2,6,2,9} {9,15,2,2,17,9}
19 7 893871738 {0,1,0,0,0,0,3}
{0,0,1,0,1,0,2} {0,0,1,0,1,1,2} {0,1,0,1,1,1,2} {0,1,1,1,1,1,2} {1,1,1,1,1,1,10} {0,0,0,0,1,4,14} {0,0,0,11,13,12,13} {0,0,9,3,17,4,14} {0,5,7,15,8,6,13} {2,7,11,6,1,14,3}
19 8 16983563040 {0,0,0,0,0,0,1,5}
{0,1,0,0,1,0,0,4} {0,0,0,0,1,1,1,4} {1,0,1,1,0,1,0,4} {0,1,1,1,1,0,1,4} {1,1,1,0,1,1,1,5} {1,1,1,1,1,1,2,5} {0,0,0,0,0,9,4,9} {0,0,0,0,10,18,16,5} {0,0,0,3,11,15,4,5} {0,0,2,18,13,9,4,16} {0,1,15,15,18,15,18,9} {4,4,18,1,4,5,2,6}
23 2 528 {1,4}
23 3 12166 {1,0,5} {1,1,5} {0,1,10} {4,4,14}
23 4 279840 {1,0,0,3}
{0,1,1,2} {1,1,1,13} {0,0,1,12} {0,1,5,9} {8,1,2,6}
23 5 6436342 {0,0,0,1,5}
{0,1,0,1,7} {1,0,1,1,5} {1,1,1,2,11} {0,0,1,18,10} {0,7,9,11,5} {8,14,15,18,21}
23 6 148035888 {0,0,0,0,1,8}
{0,0,1,1,0,2} {1,0,1,0,1,2} {0,1,1,1,1,4} {1,1,1,1,5,3} {0,0,0,16,1,12} {0,0,5,12,16,2} {0,14,5,1,15,8} {3,2,8,3,2,12}
23 7 3404825446 {0,0,1,0,0,0,7}
{0,0,1,0,0,1,5} {0,0,1,1,1,0,5} {1,0,1,1,0,1,5} {1,1,0,1,1,1,5} {1,1,1,1,1,1,7} {0,0,0,0,4,17,15} {0,0,0,7,9,11,5} {0,0,8,14,15,18,21} {0,4,21,3,11,12,15} {8,14,16,6,12,1,21}
23 8 78310985280 {0,0,0,0,1,0,0,8}
{0,0,0,0,1,1,0,2} {0,0,0,1,1,1,0,3} {0,0,1,1,0,1,1,2} {0,1,1,1,1,0,1,3} {0,1,1,1,1,1,1,4} {1,1,1,1,1,1,1,4} {0,0,0,0,0,5,8,16} {0,0,0,0,9,19,19,9} {0,0,0,16,15,10,1,12} {0,0,5,12,16,14,8,16} {0,14,18,15,12,17,10,9} {5,12,16,14,9,13,16,2}
29 2 840 {1,15}
29 3 24388 {0,1,3} {1,1,18} {10,10,8}
29 4 707280 {0,0,1,3} {1,1,0,10} {1,1,1,8} {0,17,1,19} {3,2,18,14}
29 5 20511148 {0,1,0,0,2}
{0,1,0,1,2} {1,1,1,0,3} {1,1,1,1,10} {0,0,0,1,11} {0,0,4,7,26} {0,3,19,26,15} {1,6,22,15,11}
29 6 594823320 {1,0,0,0,0,18}
{0,0,1,1,0,2} {1,1,1,0,0,3} {1,1,1,1,0,8} {1,1,1,1,2,11} {0,0,0,4,7,26} {0,0,2,24,16,3} {0,3,19,28,19,15} {1,24,3,2,13,3}
29 7 17249876308 {0,0,1,0,0,0,2}
{0,0,1,0,1,0,2} {0,0,1,0,1,1,2} {1,0,0,1,1,1,2} {0,1,1,1,1,1,2} {1,1,1,1,1,1,3} {0,0,0,0,28,17,10} {0,0,0,9,18,20,14} {0,0,13,16,25,8,3} {0,11,20,27,19,17,19} {4,26,17,21,24,23,27}
31 2 960 {1,7}
31 3 29790 {0,1,3} {1,1,12} {1,25,3}
31 4 923520 {1,0,0,18}
{1,0,1,7} {1,1,1,10} {3,0,0,10} {0,6,1,10} {5,16,28,19}
31 5 28629150 {1,0,0,0,3}
{0,0,1,1,3} {1,0,1,1,3} {1,1,1,1,21} {0,0,0,1,12} {0,0,1,25,3} {0,25,10,1,21} {1,25,22,19,3}
31 6 887503680 {1,0,0,0,0,18}
{0,0,1,1,0,7} {1,0,0,1,1,7} {1,1,1,1,0,9} {1,1,1,1,1,10} {0,0,0,23,14,9} {0,0,24,2,29,19} {0,17,9,7,19,28} {30,27,5,14,17,20}
31 7 27512614110 {0,0,0,0,0,1,3}
{0,0,0,1,0,1,3} {0,0,1,1,1,0,3} {0,1,1,0,1,1,3} {0,1,1,1,1,1,12} {1,1,1,1,1,1,11} {0,0,0,0,2,14,24} {0,0,0,1,7,6,12} {0,0,25,10,8,8,11} {0,1,25,22,20,7,3} {7,12,18,22,15,6,12}
37 2 1368 {1,15}
37 3 50652 {0,1,2} {1,2,5} {3,2,17}
37 4 1874160 {1,0,0,15}
{1,0,1,2} {1,1,1,13} {0,0,1,17} {0,3,24,18} {10,17,28,5}
37 5 69343956 {0,0,1,0,2}
{1,0,1,0,2} {0,1,1,1,5} {1,1,1,2,5} {0,0,0,1,13} {0,0,6,4,22} {0,8,23,4,2} {3,25,15,28,18}
37 6 2565726408 {0,0,0,0,1,17}
{0,0,0,1,1,5} {0,1,1,0,1,5} {0,1,1,1,1,2} {1,1,1,1,1,15} {0,0,0,1,30,15} {0,0,8,23,4,2} {0,3,25,15,28,18} {19,27,33,5,31,20}
37 7 94931877132 {0,0,1,0,0,0,2}
{0,1,0,1,0,0,2} {1,0,0,1,0,1,2} {0,1,1,0,1,1,2} {1,0,1,1,1,1,2} {1,1,1,1,1,1,17} {0,0,0,0,14,2,35} {0,0,0,6,28,15,35} {0,0,6,6,15,20,22} {0,6,28,24,27,15,35} {3,25,15,32,24,2,18}
41 2 1680 {1,7}
41 3 68920 {1,0,11} {1,1,7} {0,1,13} {3,25,6}
41 4 2825760 {0,0,1,7} {1,1,0,6} {1,1,1,15} {0,13,9,22} {2,18,26,17}
41 5 115856200 {0,0,0,1,7}
{0,1,0,1,6} {1,0,1,1,7} {1,1,1,1,7} {0,0,7,9,12} {0,3,28,2,19} {1,33,39,19,30}
41 6 4750104240 {1,0,0,0,0,6}
{0,0,0,1,1,6} {0,0,1,1,1,6} {0,1,1,1,1,6} {1,1,1,1,1,13} {0,0,0,13,9,22} {0,0,2,18,26,17} {0,4,37,23,29,35} {40,38,12,34,16,11}
41 7 194754273880 {0,1,0,0,0,0,6}
{1,0,0,1,0,0,7} {1,0,1,0,0,1,6} {0,0,1,1,1,1,6} {1,1,1,1,1,0,6} {1,1,1,1,1,1,15} {0,0,0,0,17,17,29} {0,0,0,3,28,2,19} {0,0,16,2,23,2,13} {0,4,12,34,36,25,7} {11,29,21,6,29,1,19}
43 2 1848 {1,9}
43 3 79506 {1,0,19} {1,1,3} {0,1,20} {2,42,19}
43 4 3418800 {0,0,1,9} {0,1,1,9} {1,1,1,9} {0,25,27,15} {16,2,22,40}
43 5 147008442 {0,1,0,0,3}
{0,0,1,1,5} {0,1,1,1,5} {1,1,1,1,5} {0,0,0,1,33} {0,0,2,17,18} {0,11,30,36,33} {1,9,28,17,30}
43 6 6321363048 {0,0,0,0,1,17}
{1,1,0,0,0,13} {0,1,0,1,1,13} {1,1,1,0,1,10} {1,1,1,1,1,13} {0,0,0,15,21,40} {0,0,6,7,12,24} {0,14,8,32,18,9} {6,33,12,13,38,25}
43 7 271818611106 {0,0,1,0,0,0,5}
{0,0,0,1,1,0,3} {0,0,1,1,0,1,3} {0,1,0,1,1,1,3} {1,1,0,1,1,1,3} {1,1,1,1,1,1,12} {0,0,0,0,11,39,34} {0,0,0,3,3,22,19} {0,0,1,9,28,17,30} {0,29,1,31,39,27,19} {19,6,18,24,6,9,3}
47 2 2208 {1,8}
47 3 103822 {0,1,5} {1,1,11} {4,12,22}
47 4 4879680 {0,0,1,8} {1,1,0,3} {1,1,1,9} {0,1,10,17} {24,3,36,24}
47 5 229345006 {0,0,1,0,5}
{1,1,0,0,5} {1,0,1,1,5} {1,1,1,1,19} {0,0,0,1,23} {0,0,4,12,22} {0,6,7,36,41} {6,36,16,27,11}
47 6 10779215328 {0,0,0,0,1,8}
{1,1,0,0,0,3} {0,1,0,1,1,2} {1,1,0,1,1,8} {1,1,1,1,1,14} {0,0,0,6,4,25} {0,0,10,22,32,2} {0,5,25,23,5,9} {30,12,31,29,13,18}
53 2 2808 {1,5}
53 3 148876 {1,0,2} {1,1,5} {0,1,8} {3,35,41}
53 4 7890480 {0,0,1,19} {0,1,1,2} {1,1,1,8} {0,6,7,45} {3,4,7,5}
53 5 418195492 {0,1,0,0,2}
{1,0,1,0,2} {1,1,1,0,14} {1,1,1,1,31} {0,0,0,1,3} {0,0,9,11,50} {0,19,7,33,31} {9,45,34,11,51}
53 6 22164361128 {1,0,0,0,0,8}
{0,0,1,0,1,2} {1,1,0,1,0,2} {1,1,1,0,1,8} {1,1,1,1,1,8} {0,0,0,2,23,39} {0,0,37,3,29,8} {0,30,46,17,24,33} {11,38,3,44,36,2}
59 2 3480 {1,3}
59 3 205378 {1,0,6} {1,1,6} {0,1,8} {3,1,44}
59 4 12117360 {1,0,0,4}
{1,0,1,4} {1,1,1,27} {0,0,1,5} {0,7,14,51} {5,31,51,9}
59 5 714924298 {0,0,0,1,2}
{0,1,0,1,6} {0,1,1,1,2} {1,1,1,1,8} {0,0,1,47,42} {0,42,36,34,11} {1,12,56,2,2}
59 6 42180533640 {0,0,0,0,1,9}
{0,1,0,0,1,3} {1,1,1,0,0,3} {1,1,1,1,0,7} {1,1,1,1,1,25} {0,0,0,15,41,7} {0,0,2,26,38,4} {0,17,52,46,25,29} {35,48,19,43,36,19}
61 2 3720 {1,7}
61 3 226980 {1,0,6} {1,1,6} {0,1,10} {6,46,31}
61 4 13845840 {1,0,0,7}
{1,1,0,2} {1,1,1,51} {0,0,1,31} {0,6,46,31} {6,46,58,31}
61 5 844596300 {0,0,0,1,6}
{0,0,1,1,6} {0,1,1,1,2} {1,1,1,1,7} {0,0,30,50,10} {0,14,11,46,43} {3,41,42,19,26}
61 6 51520374360 {1,0,0,0,0,17}
{0,0,1,1,0,2} {0,0,1,1,1,7} {0,1,1,1,1,2} {1,1,1,1,1,26} {0,0,0,6,46,31} {0,0,19,8,18,51} {0,14,49,10,49,44} {1,50,27,34,47,43}
67 2 4488 {1,10}
67 3 300762 {1,0,11} {1,1,13} {0,1,13} {3,42,28}
67 4 20151120 {1,0,0,6}
{1,0,1,10} {1,1,1,4} {0,0,1,60} {0,2,28,26} {10,32,28,39}
67 5 1350125106 {0,0,1,0,2}
{0,1,1,0,2} {1,0,1,1,2} {1,1,1,1,34} {0,0,0,1,12} {0,0,5,30,31} {0,24,5,50,61} {11,48,2,64,41}
67 6 90458382168 {1,1,0,0,0,4}
{1,0,1,1,0,4} {1,1,1,0,1,4} {1,1,1,1,1,26} {0,0,0,15,10,47} {0,0,8,42,4,36} {0,6,51,47,50,33} {10,32,30,48,50,39}
71 2 5040 {1,3}
71 3 357910 {0,1,21} {1,1,7} {11,46,42}
71 4 25411680 {1,0,0,6}
{1,0,1,2} {1,1,1,6} {0,0,1,10} {0,7,68,36} {10,34,20,40}
71 5 1804229350 {0,1,0,0,7}
{0,0,1,1,7} {1,1,0,1,11} {1,1,1,1,13} {0,0,0,1,33} {0,0,49,10,33} {0,4,64,68,31} {3,48,33,62,53}
71 6 128100283920 {1,0,0,0,0,15}
{0,0,0,1,1,4} {1,0,1,0,1,2} {0,1,1,1,1,4} {1,1,1,1,1,8} {0,0,0,15,67,49} {0,0,10,34,20,40} {0,19,53,21,13,9} {14,57,14,37,25,24}
73 2 5328 {1,5}
73 3 389016 {1,0,5} {1,1,33} {0,1,14} {7,23,60}
73 4 28398240 {1,0,0,26}
{1,0,1,14} {1,1,1,11} {0,0,1,34} {0,6,51,59} {17,64,70,5}
73 5 2073071592 {0,0,0,1,5}
{1,0,0,1,5} {1,1,0,1,13} {1,1,1,1,14} {0,0,6,51,59} {0,3,5,21,53} {6,56,23,61,11}
73 6 151334226288 {0,0,0,0,1,11}
{0,0,0,1,1,5} {0,1,1,1,0,13} {1,1,1,1,0,15} {1,1,1,1,1,5} {0,0,0,6,7,58} {0,0,3,5,21,53} {0,29,2,19,25,47} {30,63,55,43,48,26}
79 2 6240 {1,4}
79 3 493038 {1,0,28} {1,1,28} {0,1,29} {17,17,28}
79 4 38950080 {1,0,0,9}
{1,0,1,2} {1,1,1,4} {0,0,1,11} {0,3,5,5} {14,63,46,50}
79 5 3077056398 {0,1,0,0,3}
{1,1,0,0,3} {0,1,1,1,3} {1,1,1,1,48} {0,0,0,1,37} {0,0,4,23,7} {0,1,65,22,29} {3,53,70,66,6}
79 6 243087455520 {0,0,0,0,1,36}
{1,0,0,0,1,4} {0,1,0,1,1,2} {1,0,1,1,1,9} {1,1,1,1,1,72} {0,0,0,7,77,13} {0,0,3,5,54,31} {0,12,26,62,36,20} {22,66,24,42,6,11}
83 2 6888 {1,21}
83 3 571786 {1,0,13} {1,1,14} {0,1,19} {3,3,60}
83 4 47458320 {1,0,0,12}
{1,0,1,10} {1,1,1,61} {0,0,1,16} {0,12,15,75} {1,68,47,3}
83 5 3939040642 {1,0,0,0,2}
{1,0,1,0,2} {1,0,1,1,5} {1,1,1,1,52} {0,0,0,1,8} {0,0,3,3,60} {0,1,17,74,2} {3,56,50,71,6}
83 6 326940373368 {0,0,0,0,1,12}
{0,1,1,0,0,10} {0,1,0,1,1,3} {1,0,1,1,1,12} {1,1,1,1,1,9} {0,0,0,9,11,70} {0,0,7,32,50,12} {0,1,68,47,73,3} {12,78,65,64,6,48}
89 2 7920 {1,15}
89 3 704968 {1,0,6} {1,1,24} {0,1,7} {7,85,13}
89 4 62742240 {0,0,1,23} {1,1,0,3} {1,1,1,24} {0,4,25,7} {1,19,12,31}
89 5 5584059448 {0,1,0,0,3}
{0,1,0,1,6} {1,0,1,1,7} {1,1,1,1,3} {0,0,0,1,7} {0,0,3,59,6} {0,13,50,76,51} {1,19,12,31,61}
89 6 496981290960 {1,0,0,0,0,14}
{0,0,0,1,1,3} {1,1,0,1,0,3} {1,0,1,1,1,15} {1,1,1,1,1,26} {0,0,0,3,59,6} {0,0,40,67,77,7} {0,14,17,23,27,82} {2,39,80,41,58,63}
97 2 9408 {1,7}
97 3 912672 {0,1,5} {1,1,5} {4,27,71}
97 4 88529280 {0,0,1,26} {1,0,1,15} {1,1,1,7} {0,28,84,15} {4,29,38,39}
97 5 8587340256 {0,0,0,1,5}
{0,1,0,1,13} {1,1,1,0,5} {1,1,1,1,7} {0,0,7,34,76} {0,3,66,7,38} {3,6,74,94,37}
97 6 832972004928 {1,0,0,0,0,7}
{1,0,1,0,0,5} {1,0,0,1,1,5} {1,1,1,0,1,10} {1,1,1,1,1,37} {0,0,0,42,38,37} {0,0,3,6,72,37} {0,4,29,42,54,39} {24,8,4,24,54,71}
101 2 10200 {1,7}
101 3 1030300 {0,1,11} {1,1,8} {3,4,38}
101 4 104060400 {0,0,1,28} {0,1,1,3} {1,1,1,3} {0,4,26,40} {1,83,41,3}
101 5 10510100500 {0,0,0,1,2}
{0,0,1,1,2} {1,1,0,1,3} {1,1,1,1,8} {0,0,1,21,35} {0,16,66,61,27} {7,39,64,42,12}
103 2 10608 {1,16}
103 3 1092726 {0,1,5} {1,1,6} {3,70,6}
103 4 112550880 {0,0,1,15} {1,0,1,7} {1,1,1,15} {0,9,25,15} {1,22,2,36}
103 5 11592740742 {0,0,1,0,5}
{1,1,0,0,5} {0,1,1,1,5} {1,1,1,1,53} {0,0,0,1,43} {0,0,6,79,11} {0,8,64,50,48} {1,22,2,35,70}
107 2 11448 {1,4}
107 3 1225042 {0,1,17} {1,1,5} {1,22,73}
107 4 131079600 {1,0,0,19}
{1,0,1,10} {1,1,1,30} {0,0,1,23} {0,39,25,29} {17,95,63,100}
107 5 14025517306 {1,0,0,0,6}
{0,1,0,1,2} {1,1,1,0,5} {1,1,1,1,7} {0,0,0,1,8} {0,0,1,87,74} {0,40,81,48,31} {33,102,101,80,20}
109 2 11880 {1,10}
109 3 1295028 {1,0,6} {1,1,6} {0,1,10} {3,71,6}
109 4 141158160 {1,0,0,6}
{1,1,0,6} {1,1,1,47} {0,0,1,13} {0,24,47,40} {29,2,64,11}
109 5 15386239548 {1,0,0,0,6}
{1,1,0,0,6} {0,1,1,1,6} {1,1,1,1,6} {0,0,0,1,24} {0,0,3,71,6} {0,4,32,103,79} {11,77,104,55,91}
113 2 12768 {1,5}
113 3 1442896 {0,1,5} {1,1,6} {3,7,5}
113 4 163047360 {0,0,1,6} {0,1,1,3} {1,1,1,27} {0,12,34,20} {20,41,81,33}
113 5 18424351792 {0,1,0,0,3}
{0,1,1,0,3} {0,1,1,1,3} {1,1,1,1,5} {0,0,0,1,17} {0,0,1,93,3} {0,11,80,81,19} {3,7,83,7,5}
127 2 16128 {1,11}
127 3 2048382 {0,1,3} {1,1,6} {7,117,97}
127 4 260144640 {0,0,1,9} {1,1,0,9} {1,1,1,31} {0,2,54,88} {1,26,121,44}
127 5 33038369406 {0,0,1,0,3}
{0,0,1,1,3} {0,1,1,1,6} {1,1,1,1,7} {0,0,0,1,78} {0,0,4,110,92} {0,2,56,87,46} {4,38,41,21,7}
131 2 17160 {1,4}
131 3 2248090 {0,1,2} {1,1,6} {3,87,93}
131 4 294499920 {1,0,0,3}
{0,1,1,3} {1,1,1,3} {0,0,1,5} {0,2,57,91} {1,108,16,46}
131 5 38579489650 {0,0,1,0,2}
{1,0,1,0,2} {0,1,1,1,6} {1,1,1,1,8} {0,0,0,1,17} {0,0,4,117,95} {0,8,81,110,57} {6,100,115,67,98}
137 2 18768 {1,5}
137 3 2571352 {0,1,5} {1,1,3} {14,109,24}
137 4 352275360 {0,0,1,3} {1,0,1,12} {1,1,1,6} {0,1,113,3} {4,125,45,53}
137 5 48261724456 {0,1,0,0,3}
{1,1,0,0,3} {1,0,1,1,5} {1,1,1,1,13} {0,0,0,1,35} {0,0,12,45,20} {0,6,21,59,55} {10,65,110,96,62}
139 2 19320 {1,24}
139 3 2685618 {0,1,2} {1,1,3} {7,51,58}
139 4 373301040 {1,0,0,9}
{1,0,1,7} {1,1,1,4} {0,0,1,46} {0,12,41,66} {3,9,39,5}
139 5 51888844698 {0,0,1,0,3}
{0,1,1,0,3} {0,1,1,1,21} {1,1,1,1,12} {0,0,0,1,12} {0,0,4,40,53} {0,13,79,12,22} {9,34,26,16,61}
149 2 22200 {1,10}
149 3 3307948 {1,0,2} {1,1,3} {0,1,18} {5,76,58}
149 4 492884400 {1,0,0,3}
{1,0,1,8} {1,1,1,21} {0,0,1,12} {0,6,110,60} {16,6,101,75}
149 5 73439775748 {0,0,1,0,8}
{0,1,0,1,2} {0,1,1,1,3} {1,1,1,1,12} {0,0,0,1,13} {0,0,1,31,51} {0,6,23,33,59} {5,79,115,53,108}
151 2 22800 {1,10}
151 3 3442950 {0,1,7} {1,1,7} {1,31,102}
151 4 519885600 {1,0,0,5}
{1,1,0,11} {1,1,1,5} {0,0,1,17} {0,1,123,103} {3,10,1,5}
151 5 78502725750 {1,0,0,0,6}
{0,1,1,0,6} {1,1,1,0,14} {1,1,1,1,7} {0,0,0,1,48} {0,0,2,65,104} {0,32,16,136,52} {3,102,109,45,6}
157 2 24648 {1,5}
157 3 3869892 {1,0,5} {1,1,18} {0,1,15} {3,105,6}
157 4 607573200 {0,0,1,38} {1,1,0,6} {1,1,1,34} {0,15,153,26} {15,66,90,77}
157 5 95388992556 {0,0,1,0,6}
{1,0,0,1,5} {0,1,1,1,5} {1,1,1,1,18} {0,0,0,1,24} {0,0,9,33,15} {0,19,117,70,84} {19,117,84,113,136}
163 2 26568 {1,4}
163 3 4330746 {1,0,2} {1,1,7} {0,1,3} {7,62,66}
163 4 705911760 {0,0,1,4} {0,1,1,9} {1,1,1,34} {0,9,38,69} {4,149,13,62}
163 5 115063617042 {0,1,0,0,2}
{0,0,1,1,3} {0,1,1,1,2} {1,1,1,1,18} {0,0,0,1,66} {0,0,17,42,82} {0,9,140,3,70} {3,110,140,45,114}
167 2 27888 {1,4}
167 3 4657462 {1,0,10} {1,1,17} {0,1,17} {7,161,13}
167 4 777796320 {0,0,1,8} {0,1,1,3} {1,1,1,8} {0,4,47,7} {18,85,121,141}
167 5 129891985606 {0,1,0,0,5}
{1,0,0,1,5} {0,1,1,1,5} {1,1,1,1,39} {0,0,0,1,17} {0,0,6,21,10} {0,5,89,55,120} {1,35,33,141,113}
173 2 29928 {1,11}
173 3 5177716 {0,1,5} {1,1,8} {2,76,61}
173 4 895745040 {0,0,1,19} {1,0,1,2} {1,1,1,5} {0,6,130,68} {9,42,50,72}
173 5 154963892092 {0,1,0,0,3}
{1,0,1,0,2} {1,0,1,1,5} {1,1,1,1,12} {0,0,0,1,48} {0,0,2,76,61} {0,25,53,172,98} {4,158,43,20,123}
179 2 32040 {1,9}
179 3 5735338 {0,1,2} {1,1,7} {1,147,122}
179 4 1026625680 {1,0,0,9}
{1,0,1,5} {1,1,1,13} {0,0,1,20} {0,30,155,169} {12,59,138,20}
179 5 183765996898 {1,0,0,0,2}
{0,0,1,1,6} {0,1,1,1,2} {1,1,1,1,8} {0,0,0,1,6} {0,0,1,147,122} {0,4,53,125,7} {8,111,141,125,133}
181 2 32760 {1,10}
181 3 5929740 {1,0,2} {1,1,21} {0,1,18} {6,26,10}
181 4 1073283120 {0,0,1,10} {0,1,1,2} {1,1,1,10} {0,28,173,47} {4,54,55,127}
181 5 194264244900 {0,0,1,0,2}
{0,1,1,0,2} {1,1,1,0,10} {1,1,1,1,54} {0,0,0,1,10} {0,0,1,38,2} {0,1,149,59,123} {1,38,15,139,2}
191 2 36480 {1,8}
191 3 6967870 {1,0,19} {1,1,29} {0,1,21} {17,159,29}
191 4 1330863360 {1,0,0,4}
{0,1,1,4} {1,1,1,8} {0,0,1,12} {0,1,40,2} {2,84,190,4}
191 5 254194901950 {0,1,0,0,19}
{0,0,1,1,19} {1,1,0,1,29} {1,1,1,1,19} {0,0,0,1,35} {0,0,25,160,42} {0,11,136,75,19} {3,12,81,17,132}
193 2 37248 {1,10}
193 3 7189056 {0,1,5} {1,1,5} {1,40,66}
193 4 1387488000 {0,0,1,5} {1,0,1,5} {1,1,1,5} {0,28,166,111} {5,103,36,73}
193 5 267785184192 {0,0,0,1,5}
{1,0,1,0,5} {1,1,0,1,5} {1,1,1,1,52} {0,0,9,38,79} {0,30,49,124,113} {9,47,33,9,15}
197 2 38808 {1,3}
197 3 7645372 {0,1,2} {1,1,12} {4,58,72}
197 4 1506138480 {0,0,1,12} {0,1,1,8} {1,1,1,31} {0,5,104,74} {16,129,137,27}
197 5 296709280756 {0,0,0,1,2}
{0,1,0,1,2} {1,1,0,1,2} {1,1,1,1,18} {0,0,1,41,67} {0,1,41,75,2} {9,169,52,124,147}
199 2 39600 {1,4}
199 3 7880598 {0,1,15} {1,1,3} {1,41,134}
199 4 1568239200 {1,0,0,4}
{1,0,1,2} {1,1,1,20} {0,0,1,9} {0,11,135,151} {8,124,43,80}
199 5 312079600998 {0,1,0,0,3}
{1,0,0,1,6} {0,1,1,1,15} {1,1,1,1,22} {0,0,0,1,6} {0,0,9,165,148} {0,3,12,178,71} {6,153,26,21,143}
211 2 44520 {1,4}
211 3 9393930 {0,1,2} {1,1,29} {13,104,22}
211 4 1982119440 {0,0,1,16} {0,1,1,9} {1,1,1,20} {0,14,152,24} {3,143,86,6}
211 5 418227202050 {0,0,1,0,17}
{0,0,1,1,2} {0,1,1,1,2} {1,1,1,1,3} {0,0,0,1,39} {0,0,17,167,29} {0,1,174,11,3} {13,120,2,1,162}
223 2 49728 {1,29}
223 3 11089566 {1,0,5} {1,1,6} {0,1,11} {1,46,150}
223 4 2472973440 {1,0,0,9}
{1,1,0,9} {1,1,1,55} {0,0,1,36} {0,2,98,152} {11,159,41,19}
223 5 551473077342 {0,0,1,0,3}
{0,1,0,1,3} {0,1,1,1,5} {1,1,1,1,5} {0,0,0,1,5} {0,0,1,46,150} {0,1,183,209,3} {6,34,81,120,158}
227 2 51528 {1,3}
227 3 11697082 {1,0,5} {1,1,6} {0,1,8} {3,12,80}
227 4 2655237840 {0,0,1,3} {1,0,1,10} {1,1,1,63} {0,9,46,90} {17,63,11,28}
227 5 602738989906 {0,0,1,0,2}
{0,1,1,0,6} {0,1,1,1,6} {1,1,1,1,14} {0,0,0,1,8} {0,0,3,12,80} {0,1,47,127,2} {3,154,60,12,6}
229 2 52440 {1,7}
229 3 12008988 {1,0,6} {1,1,6} {0,1,23} {6,167,163}
229 4 2750058480 {0,0,1,7} {0,1,1,6} {1,1,1,6} {0,3,11,157} {17,204,111,29}
229 5 629763392148 {0,0,0,1,6}
{0,0,1,1,7} {1,1,1,0,6} {1,1,1,1,7} {0,0,23,211,191} {0,6,35,54,10} {1,188,202,39,155}
233 2 54288 {1,5}
233 3 12649336 {0,1,5} {1,1,3} {1,191,158}
233 4 2947295520 {0,0,1,5} {1,1,0,5} {1,1,1,3} {0,7,229,168} {9,200,39,93}
233 5 686719856392 {0,0,0,1,3}
{0,0,1,1,3} {0,1,1,1,3} {1,1,1,1,3} {0,0,6,175,166} {0,3,14,220,82} {3,14,220,125,5}
239 2 57120 {1,5}
239 3 13651918 {1,0,7} {1,1,7} {0,1,39} {24,15,39}
239 4 3262808640 {0,0,1,5} {0,1,1,2} {1,1,1,58} {0,3,15,5} {7,92,218,12}
239 5 779811265198 {1,0,0,0,7}
{0,1,0,1,7} {0,1,1,1,13} {1,1,1,1,13} {0,0,0,1,14} {0,0,4,71,7} {0,8,149,22,14} {15,101,36,89,184}
241 2 58080 {1,14}
241 3 13997520 {1,0,13} {1,1,34} {0,1,34} {2,106,84}
241 4 3373402560 {0,0,1,13} {0,1,1,13} {1,1,1,31} {0,2,106,84} {42,148,53,69}
241 5 812990017200 {0,0,0,1,35}
{0,0,1,1,7} {0,1,1,1,13} {1,1,1,1,34} {0,0,7,90,92} {0,22,201,197,37} {14,193,159,203,104}
251 2 63000 {1,7}
251 3 15813250 {1,0,14} {1,1,19} {0,1,18} {2,110,87}
251 4 3969126000 {1,0,0,17}
{0,1,1,9} {1,1,1,21} {0,0,1,52} {0,21,134,118} {8,156,150,181}
251 5 996250626250 {0,0,0,1,6}
{0,1,0,1,6} {0,1,1,1,6} {1,1,1,1,6} {0,0,7,92,95} {0,59,230,192,14} {16,10,177,172,26}
257 2 66048 {1,19}
257 3 16974592 {0,1,3} {1,1,7} {4,233,179}
257 4 4362470400 {0,0,1,28} {0,1,1,3} {1,1,1,41} {0,56,194,7} {16,169,29,27}
257 5 1121154893056 {0,1,0,0,3}
{1,0,1,0,3} {1,1,1,0,6} {1,1,1,1,14} {0,0,0,1,6} {0,0,6,195,182} {0,24,19,177,39} {11,25,53,185,103}
509 2 259080 {1,10}
509 3 131872228 {1,0,2} {1,1,7} {0,1,15} {14,74,192}
509 4 67122964560 {1,0,0,10}
{1,1,0,2} {1,1,1,41} {0,0,1,19} {0,3,341,175} {11,49,13,18}
521 2 271440 {1,15}
521 3 141420760 {1,0,3} {1,1,6} {0,1,23} {4,153,7}
521 4 73680216480 {0,0,1,7} {0,1,1,3} {1,1,1,27} {0,45,19,73} {3,32,134,178}
1021 2 1042440 {1,34}
1021 3 1064332260 {0,1,10} {1,1,30} {6,151,10}
1021 4 1086683238480 {0,0,1,30}
{1,0,1,10} {1,1,1,40} {0,18,511,30} {6,154,291,10}
1031 2 1062960 {1,4}
1031 3 1095912790 {0,1,21} {1,1,38} {12,967,21}
1031 4 1129886087520 {1,0,0,3}
{0,1,1,2} {1,1,1,20} {0,0,1,9} {0,6,787,11} {8,642,92,357}
2039 2 4157520 {1,3}
2039 3 8477185318 {0,1,7} {1,1,13} {5,1081,1368}
2039 4 17284980865440 {1,0,0,5} {1,1,0,2} {1,1,1,3} {0,0,1,6}
2053 2 4214808 {1,32}
2053 3 8653002876 {1,0,6} {1,1,6} {0,1,32} {19,1527,1400}
2053 4 17764614906480 {0,0,1,5} {0,1,1,2}
4093 2 16752648 {1,5}
4093 3 68568592356 {0,1,2} {1,1,5} {11,2899,2747}
4099 2 16801800 {1,13}
4099 3 68870582298 {0,1,2} {1,1,10} {1,845,2}
8191 2 67092480 {1,21}
8191 3 549554511870 {0,1,17} {1,1,17} {10,3893,17}
8209 2 67387680 {1,7}
8209 3 553185473328 {1,0,7} {1,1,14} {0,1,46} {3,491,5477}
16381 2 268337160 {1,17}
16381 3 4395631034340 {1,0,2} {1,1,24} {0,1,11} {1,13498,5463}
16411 2 269320920 {1,5}
16411 3 4419825634530 {0,1,14} {1,1,10}
32749 2 1072497000 {1,7}
32749 3 35123204285748 {0,1,7}
32771 2 1073938440 {1,4}
32771 3 35194036650010 {0,1,8}
65521 2 4293001440 {1,17}
65537 2 4295098368 {1,10}
131071 2 17179607040 {1,5}