Count of Array

 You love array, don't you?

You are given two integer N$N$ and M$M$, along with an array B$B$ of length N$N$ containing pairwise distinct integers. You have to find the number of array A$A$ of length N$N$ satisfying the follow conditions:

1. 1≤Ai≤M$1\le A_i\le M$.
2. Ai≠Aj$A_i\ne A_j$ for all 1≤i<j≤N$1\le i<j\le N$.
3. Ai≠Bi$A_i\ne B_i$ for all 1≤i≤N$1\le i\le N$.

Since the answer can be very large, output it under modulo 109+7${10}^9+7$.

Input Format

• The first line of the input contains two space-separated integers N$N$ and M$M$.
• The second line of the input contains N$N$ separated integers B1,B2,…,BN$B_1,B_2,\dots ,B_N$ - the array B$B$.

Output Format

Output on a single line the number of satisfactory array modulo 109+7${10}^9+7$.

Constraints

• 1≤N≤2⋅105$1\le N\le 2\cdot {10}^5$
• 1≤M≤3⋅105$1\le M\le 3\cdot {10}^5$
• 1≤Bi≤109$1\le B_i\le {10}^9$
• Bi≠Bj$B_i\ne B_j$ for all 1≤i<j≤N$1\le i<j\le N$.

Sample Input 1 

3 4
5 1 2

Sample Output 1 

14

Explanation

All satisfactory arrays are:

• [1,2,3]$[1,2,3]$
• [2,3,1]$[2,3,1]$
• [3,2,1]$[3,2,1]$
• [1,2,4]$[1,2,4]$
• [2,4,1]$[2,4,1]$
• [4,2,1]$[4,2,1]$
• [1,3,4]$[1,3,4]$
• [1,4,3]$[1,4,3]$
• [3,4,1]$[3,4,1]$
• [4,3,1]$[4,3,1]$
• [2,3,4]$[2,3,4]$
• [2,4,3]$[2,4,3]$
• [3,2,4]$[3,2,4]$
• [4,2,3]$[4,2,3]$

Sample Input 2 

2 2
1 3

Sample Output 2 

1

Explanation

The only satisfactory array is:

• [2,1]