Make Rounddog Happy

Rounddog always carries an array $a_1, a_2, \ldots, a_n$ in his right pocket, satisfying $1 \le a_i \le n$.

A subarray is a non-empty contiguous segment of the original array. Rounddog defines a good subarray as a segment $a_l, a_{l+1}, \ldots, a_r$ in which all elements are distinct and $\max(a_l, a_{l+1}, \ldots, a_r) - (r - l + 1) \le k$.

Rounddog is not happy today. As his best friend, you want to find all good subarrays of $a$ to make him happy. For this problem, calculate the number of good subarrays of $a$.

The input contains several test cases. The first line contains a single integer $T$ ($1 \le T \le 20$), the number of test cases.

The first line of each test case contains two integers $n$ ($1 \le n \le 300\,000$) and $k$ ($1 \le k \le 300\,000$).

The second line contains $n$ integers, the $i$-th of which is $a_i$ ($1 \le a_i \le n$).

The sum of $n$ over all test cases does not exceed $1\,000\,000$.

For each test case, print a single line with a single integer: the number of good subarrays in the given array.