We Be Summing
Description
You are given an array $a$ of length $n$ and an integer $k$.
Call a non-empty array $b$ of length $m$ epic if there exists an integer $i$ where $1 \le i < m$ and $\min(b_1,\ldots,b_i) + \max(b_{i + 1},\ldots,b_m) = k$.
Count the number of epic subarrays$^{\text{∗}}$ of $a$.
$^{\text{∗}}$An array $a$ is a subarray of an array $b$ if $a$ can be obtained from $b$ by the deletion of several (possibly, zero or all) elements from the beginning and several (possibly, zero or all) elements from the end.
The first line contains an integer $t$ ($1 \le t \le 10^4$) — the number of testcases.
The first line of each testcase contains integers $n$ and $k$ ($2 \le n \le 2 \cdot 10^5$; $n < k < 2 \cdot n$) — the length of the array $a$ and $k$.
The second line of each testcase contains $n$ integers $a_1,a_2,\ldots,a_n$ ($1 \le a_i \le n$).
The sum of $n$ across all testcases does not exceed $2 \cdot 10^5$.
For each testcase, output the number of epic contiguous subarrays of $a$.
Input
The first line contains an integer $t$ ($1 \le t \le 10^4$) — the number of testcases.
The first line of each testcase contains integers $n$ and $k$ ($2 \le n \le 2 \cdot 10^5$; $n < k < 2 \cdot n$) — the length of the array $a$ and $k$.
The second line of each testcase contains $n$ integers $a_1,a_2,\ldots,a_n$ ($1 \le a_i \le n$).
The sum of $n$ across all testcases does not exceed $2 \cdot 10^5$.
Output
For each testcase, output the number of epic contiguous subarrays of $a$.
6
5 7
1 2 3 4 5
7 13
6 6 6 6 7 7 7
6 9
4 5 6 6 5 1
5 9
5 5 4 5 5
5 6
3 3 3 3 3
6 8
4 5 4 5 4 5
2
12
3
8
10
4
Note
These are all the epic subarrays in the first testcase:
- $[2, 3, 4, 5]$, because $\min(2, 3) + \max(4, 5) = 2 + 5 = 7$.
- $[3, 4]$, because $\min(3) + \max(4) = 3 + 4 = 7$.
In the second test case, every subarray that contains at least one $6$ and at least one $7$ is epic.