Factorial grows exponentially, which means that 10⁹! will have enormous amount of digits (linear of N, at least) and you won't be able to output or even store such big number.

If you want to get factorial by some modulo, you can do it in . Just precalc factorial in some checkpoints like , , , etc and then start calculating from the checkpoint.

Interesting how to find i-th number of (n!)?

http://e-maxx.ru/algo/modular_factorial O(M log N)