**Can someone please provide the editorial of this question.**

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*_{j}) 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 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

1 ≤ *T* ≤ 10, 1 ≤ *N* ≤ 10^{5}, - 2 × 10^{9} ≤ *a*, *b*, *c*, *d*, *A*_{i} ≤ 2 × 10^{9}, 1 ≤ *m* ≤ 2 × 10^{9}

Sample Input

1 2 1 -1 3 5 5 10 2 3 14 12

Sample Output

2

**Explanation**

Equation of curve: *y*^{2} = 2*x*^{3} + *x*^{2} - *x* + 3 and m = 5. Valid pairs satisfying equation of line are (*x*, *y*) = (2, 14) and (12, 14). Therefore, the answer is 2.

**Note**: This question is taken from Hackerearth Lenskart hiring challenge which has already expired.