There are n nonnegative integers a1…n which are less than p. HazelFan wants to know how many pairs i,j(1≤i<j≤n) are there, satisfying 1ai+aj≡1ai+1aj when we calculate module p,
which means the inverse element of their sum equals the sum of their
inverse elements. Notice that zero element has no inverse element.
Input
The first line contains a positive integer T(1≤T≤5), denoting the number of test cases. For each test case: The first line contains two positive integers n,p(1≤n≤105,2≤p≤1018), and it is guaranteed that p is a prime number. The second line contains n nonnegative integers a1...n(0≤ai<p).
Output
For each test case:
A single line contains a nonnegative integer, denoting the answer.