Count of Array

You love array, don't you? You are given two integer $N$ and $M$, along with an array $B$ of length $N$ containing **pairwise distinct** integers. You have to find the number of array $A$ of length $N$ satisfying the follow conditions: 1. $1 \leq A_i \leq M$. 2. $A_i \neq A_j$ for all $1 \le i \lt j \le N$. 3. $A_i \neq B_i$ for all $1 \le i \le N$. Since the answer can be very large, output it