410482: GYM104025 H Happiness Index

The government is very concerned about the happiness index of residents. In the practical work of ideological and political courses, Master Yi collected the happiness index of $$$n$$$ residents in his hometown as an integer array $$$a_1, a_2, \cdots, a_n$$$.

In this task, Master Yi wants to know how many intervals are there satisfying that the average happiness index in this interval is approximately $$$k$$$. In other words, please help him calculate how many intervals $$$[l,r]$$$ satisfy $$$\lfloor{\frac{a_l+a_{l+1}+\cdots+a_r}{r-l+1}}\rfloor=k$$$.

The first line contains a single integer $$$t\ (1\le t\le 10^4)$$$, the number of test cases. For each test case:

The first line contains $$$2$$$ integers $$$n\ (1\le n\le 2\cdot 10^5)$$$ and $$$k\ (0\le k\le 10^9)$$$, the number of the interviewed residents and the required happiness index.

The second line contains $$$n$$$ integers $$$a_1, a_2, \cdots, a_n\ (0\le a_i\le 10^9)$$$, which are the happiness indexes of each interviewed resident.

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$5\cdot 10^5$$$.

For each test case, print the answer in a single line, which is the number of subsegments satisfying the condition.

1
3 2
2 1 3

3

In the first example, the subsegments satisfying the condition are $$$[2]$$$, $$$[1,3]$$$ and $$$[2,1,3]$$$, each has an average happiness index of $$$2$$$.