Project Euler Forum

I think it's trivial to show that $m\geq n$ otherwise $S=\emptyset$.
Therefore I think there is a typo and that we are meant to instead find $F(10^4+1, 30) \mod {10^9+7}$.

Nowhere does it say the x's need to be distinct. The easiest example of a possible product is 1. I see nothing to suggest a mistake in the problem.

My mistake, thanks.