Pair Sum

You are given an integer array of size $N$ and an integer $M$. The array has $N \times (N - 1) / 2$ distinct pairs. Count how many of those pairs have a sum exactly equal to $M$.

For example, if the array is $\{1, 2, 3, 4\}$ and $M = 5$, then two pairs sum to $M$: $\{1, 4\}$ and $\{2, 3\}$.

The first line contains the number of test cases $T$. $T$ is a positive integer at most $100\,000$.

Each test case consists of two lines. The first line contains two integers $N$ and $M$ separated by a single space. $N$ is between $2$ and $20\,000$ inclusive. The second line contains the $N$ values of the array separated by single spaces. Every value is between $1$ and $1\,000\,000\,000$ inclusive, the values are distinct, and they are sorted in increasing order.

For each test case, print one line in the format Case #x: R, where $x$ is the case number starting from 1 and $R$ is the number of pairs whose sum is exactly $M$.