All that's needed is that the format specifiers and the types agree, and you can always cast to make that true. long is at least 32 bits, so %lu together with (unsigned long)k is always correct:
uint32_t k;
printf("%lu\n", (unsigned long)k);
size_t is trickier, which is why %zu was added in C99. If you can't use that, then treat it just like k (long is the biggest type in C89, size_t is very unlikely to be larger).
size_t sz;
printf("%zu\n", sz); /* C99 version */
printf("%lu\n", (unsigned long)sz); /* common C89 version */
If you don't get the format specifiers correct for the type you are passing, then printf will do the equivalent of reading too much or too little memory out of the array. As long as you use explicit casts to match up types, it's portable.