Permutations with Duplicates in C

Calculating permutations has some fairly nifty algorithms out there. I recently ran into a permutation problem for which I couldn't find an existing algorithm. I admit that I didn't look too hard though. Basically, I needed the permutations of the elements of a set of size N over K slots. However, the permutations should include duplicate elements from the set, as K > N is valid configuration. This corresponds to N^K permutations. Most algorithms I found did not permit duplicate elements.

As an example of an application for such a permutation algorithm, imagine the set of all function signatures of arity K-1 over N types. This corresponds to K slots with N possible choices for each slot.

I devised a fairly simple implementation of such a permutation algorithm. Essentially, N forms the base of an arbitrary-precision integer of size K. In other words, we have an array of elements with a maximum of N which index our set. To permute, we simply increment the first element and propagate any overflow across the rest of the array. If the carry is 1 when we're done iterating over the whole array, then we're done generating permutations.

Calculating permutations has been reduced to counting! Here is the C code:

#include <stdio.h>

void print(const unsigned *slots, const unsigned K)
{
  unsigned i;
  for (i = 0; i < K; ++i) {
    printf("%4d", slots[i] );
  }
  printf("\n");
}

unsigned incr(unsigned *slots, const unsigned K, const unsigned N) {
  unsigned i, carry;
  print(slots, K);
  for (i=0, carry=1; i < K; ++i) {
    unsigned b = slots[i] + carry;
    carry = b/N;
    slots[i] = b % N;
  }
  return !carry;
}

void count(const unsigned N, const unsigned K) {
  unsigned i;
  unsigned *slots = calloc(K, sizeof(unsigned));
  while(incr(slots, K, N)) {
  }
}

//output:
//   0   0   0
//   1   0   0
//   0   1   0
//   1   1   0
//   0   0   1
//   1   0   1
//   0   1   1
//   1   1   1
int main(int argc, char ** argv) {
  count(2, 3);
  getchar();
}

The only assumption is that N is less than UINT_MAX. Also, for some insane reason that I cannot fathom, I can't get the slots to print in reverse order. The trivial reversal of the print loop induces an access violation under Windows:

void print(const unsigned *slots, const unsigned K)
{
  unsigned i;
  for (i = K-1; i >= 0; --i) {
    printf("%4d", slots[i] );
  }
  printf("\n");
}

The mind boggles.

[Edit: a commenter pointed out the problem, so the solution can be found in the comments.]