Inverse of sum

Problem Description

There are $n$ nonnegative integers $a_{1¡­n}$ which are less than $p$. HazelFan wants to know how many pairs $i,j(1\leq i<j\leq n)$ are there, satisfying $\frac{1}{a_i+a_j}\equiv\frac{1}{a_i}+\frac{1}{a_j}$ 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 $T(1\leq T\leq5)$, denoting the number of test cases. For each test case: The first line contains two positive integers $n,p(1\leq n\leq10^5,2\leq p\leq10^{18})$, and it is guaranteed that $p$ is a prime number. The second line contains $n$ nonnegative integers $a_{1...n}(0\leq a_i<p)$.

Output

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

Sample Input

2

5 7

1 2 3 4 5

6 7

1 2 3 4 5 6

Sample Output

4

6

Source

2017 Multi-University Training Contest - Team 7

https://acm.hdu.edu.cn/showproblem.php?pid=6128