D. Divisible Pairstime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputPolycarp has two favorite integers x and y (they can be equal), and he has found an array a of length n.Polycarp considers a pair of indices \langle i, j \rangle (1 \le i < j \le n) beautiful if:   a_i + a_j is divisible by x;  a_i - a_j is divisible by y. For example, if x=5, y=2, n=6, a=[1, 2, 7, 4, 9, 6], then the only beautiful pairs are:   \langle 1, 5 \rangle: a_1 + a_5 = 1 + 9 = 10 (10 is divisible by 5) and a_1 - a_5 = 1 - 9 = -8 (-8 is divisible by 2);  \langle 4, 6 \rangle: a_4 + a_6 = 4 + 6 = 10 (10 is divisible by 5) and a_4 - a_6 = 4 - 6 = -2 (-2 is divisible by 2).  Find the number of beautiful pairs in the array a.InputThe first line of the input contains a single integer t (1 \le t \le 10^4) — the number of test cases. Then the descriptions of the test cases follow.The first line of each test case contains three integers n, x, and y (2 \le n \le 2 \cdot 10^5, 1 \le x, y \le 10^9) — the size of the array and Polycarp's favorite integers.The second line of each test case contains n integers a_1, a_2, \dots, a_n (1 \le a_i \le 10^9) — the elements of the array.It is guaranteed that the sum of n over all test cases does not exceed 2 \cdot 10^5.OutputFor each test case, output a single integer — the number of beautiful pairs in the array a.ExampleInput
76 5 21 2 7 4 9 67 9 51 10 15 3 8 12 159 4 1014 10 2 2 11 11 13 5 69 5 610 7 6 7 9 7 7 10 109 6 24 9 7 1 2 2 13 3 159 2 314 6 1 15 12 15 8 2 1510 5 713 3 3 2 12 11 3 7 13 14Output
2
0
1
3
5
7
0

76 5 21 2 7 4 9 67 9 51 10 15 3 8 12 159 4 1014 10 2 2 11 11 13 5 69 5 610 7 6 7 9 7 7 10 109 6 24 9 7 1 2 2 13 3 159 2 314 6 1 15 12 15 8 2 1510 5 713 3 3 2 12 11 3 7 13 14
2 0 1 3 5 7 0 
['combinatorics', 'math', 'number theory', '*1300']