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
\(1 \le T \le 10\\ 1 \le N \le10^5\\ -2 \times10^9 \le a,b,c,d,A_i \le 2 \times 10^9\\ 1 \le m \le 2 \times 10^9\)
Equation of curve: \(y^2=2x^3+x^2-x+3\) and m$$=5$$.
Valid pairs satisfying equation of line are $$(x,y) = (2,14)$$ and $$(12,14)$$. Therefore, the answer is $$2$$.