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 ≤ A i ≤ M 1 ≤ A i ≤ M . A i ≠ A j A i ≠ A j for all 1 ≤ i < j ≤ N 1 ≤ i < j ≤ N . A i ≠ B i A i ≠ B i for all 1 ≤ i ≤ N 1 ≤ i ≤ N . Since the answer can be very large, output it under modulo 10 9 + 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 B 1 , B 2 , … , B N B 1 , B 2 , … , B N - the array B B . Output Format Output on a single line the number of satisfactory array modulo 10 9 + 7 10 9 + 7 . Constraints 1 ≤ N ≤ 2 ⋅ 10 5 1 ≤ N ≤ 2 ⋅ 10 5 1 ≤ M ≤ 3 ⋅ 10 5 1 ≤ M ≤...