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 1/(ai+aj)≡1/ai+1/aj 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.

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≤10^5,2≤p≤10^18), and it is guaranteed that p is a prime number.
The second line contains n nonnegative integers a1...n(0≤ai<p).

For each test case:
A single line contains a nonnegative integer, denoting the answer.