For the http://mirror.codeforces.com/contest/560/problem/E

Number of distinct ways (only Down and Right) modulo p in a grid of w and h celss is: modC(w+h-2, h-1, p) where

modC(n, k, p) = C(n, k) mod p = modFact(n, p) * ((modInvFact(k, p) * modInvFact(n-k, p) mod p) mod p

modFact(n+1, p) = modFact(n, p) * (n+1) mod p, where modFact(0, p) = 1

modInvFact(n-1, p) = modInvFact(n, p) * n mod p, where modInvFact(N, p) = modExp(modFact(N, p), p-2, p)

modExp(n, e, p): res = 1 b = n mod p while e > 0 if (e mod 2 == 1): res := (res * b) mod p e >>= 1 b = (b * b) mod p return res