You are given with integers \(a, b, c, d, m\). These represent the modular equation of a curve \( y^2 mod\ m = (ax^3+bx^2+cx+d)\ mod\ m\)

Also, you are provided with an array \(A\) of size \(N\). Now, your task is to find the number of pairs in the array that satisfy the given modular equation.

If $$(A_i, A_j)$$ is a pair then \( A_j^2 mod \ m = (aA_i^3+bA_i^2+cA_i+d)\ mod\ m\).

Since the answer could be very large output it modulo $$10^9 + 7$$.

Note: A pair is counted different from some other pair if either $$A_i$$ of the two pairs is different or $$A_j$$ of the two pairs is different. Also for the convenience of calculations, we may count \((A_i,A_i)\) as a valid pair if it satisfies given constraints.

Input Format
First line of the input contains number of test cases \(T\).
First line for each test case consists of $$5$$ space-separated integers \(a, b, c, d, m\), corresponding to modular equation given.
Next line contains a single integer \(N\).
Next line contains \(N\) space-separated integers corresponding to values of array \(A\).

Output Format
For each test case, output a single line corresponding to number of valid pairs in the array mod \(10^9+7\).

Constraints