Component Count

You are given an $N\times M$ grid, with each cell initially painted white. You need to paint exactly $K$ of these cells black, such that every black cell is reachable from every other black cell, by travelling horizontally, vertically or diagonally through other black cells. Find the number of ways to paint the grid in such a manner, modulo $10^9 + 7$. ### Input - The first line of input will