Pairs With a Given Sum

A number $s$ and an array of $n$ different non-negative integers are given. Your task is to count the pairs of elements of the array whose sum is exactly $s$.

Input

The first line contains a single integer $t$ - the number of testcases.

• The first line of each testcase contains two integers $n$ and $s$ - the number of elements and the target sum.
• The next line contains $n$ different integers $a_0,a_1,\dots ,a_{n-1}$ - the elements of the array.

Output

For every testcase print a single line with the number of pairs of different elements whose sum equals $s$.

Example

2
6 7
2 5 4 7 0 6
5 8
1 2 3 4 6

2
1

In the first testcase the pairs are $(2,5)$ and $(7,0)$. In the second testcase the only pair is $(2,6)$ - note that $4$ cannot be paired with itself.

Constraints

$1\le t\le 1000$
$1\le n\le 2\cdot 10^5$
$0\le a_i\le 10^9$
$0\le s\le 2\cdot 10^9$
$n_1+n_2+\dots +n_t\le 2\cdot 10^5$

This problem was adapted, with permission, from Broj parova datog zbira, authored by Društvo matematičara Srbije and Fondacija Petlja.