Gold Rush

On the two dimensional co-ordinate plane, a mythical creature starts from the square $(1,1)$ and moves to the square $(N,M)$, using only down and right moves (that is, it can move from $(x, y)$ to $(x+1, y)$ or $(x, y+1)$). The creature drops a single gold coin on every square on its path (including $(1, 1)$ and $(N, M)$). Also, it chooses any path uniformly at random, out of all possible paths