Function Function

Consider a bijective function $ƒ$ $$ f: {1, 2, 3, \dots, n} \rightarrow {1, 2, 3, \dots, n} $$ We have $M$ different color. We have to associate a color to every $x \in {1, 2, 3, ... n}$ with one of the color such that $x$ and$ƒ(ƒ(x))$ has same color . Let G be an array, where G[x] = pair(ƒ[x], color[x]). Find the number of distinct arrays G modulo 1000000007. Input Format: First and the only