i'm trying to solve this problem but i can't find any algorithm better than O(n^2) !

your help will be greatly appreciated.

i'm trying to calculate nCr mod prime power , i found this comment which is really helpful but the formula as i understand doesn't apply to some numbers and i don't know how it works , could anyone explain it in more details ?

this is a solution for problem H from last contest , can anyone explain to me how this solution works ?