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 $$$\langle i, j \rangle$$$ ($$$1 \le i \lt j \le n$$$) 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 $$$a$$$.

Input

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 $$$2 \cdot 10^5$$$.

Output

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

Divisible Pairs

Examples