CF1931D Divisible Pairs

Polycarp 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 $ .

The 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 $ .

For each test case, output a single integer — the number of beautiful pairs in the array $ a $ .