Monke is a talented but lazy programmer. He doesn't practice a lot. He lives in a weird country where every month consists of $$$n$$$ days. He also has a favorite number $$$k$$$, because he is weird. As Monke is lazy, he didn't solve any problems in the last month. But he cares about his maximum problem-solving streak. So this month, he solved some problems but lost count of how many problems he solved on each day of the month.
Luckily he maintained an array $$$a$$$ of size $$$n$$$, where for all $$$i\ (i \lt k)$$$, $$$a_i$$$ is the no of problems solved in the last $$$i$$$ days, and for all $$$i\ (i \ge k)$$$, $$$a_i$$$ is the number of problems solved in the last $$$k$$$ days on the $$$i$$$'th day of this month. Formally, $$$a_i$$$ $$$(1 \le i \le n)$$$ means the total number of problems he has solved in days $$$[i,\ i - 1,\ i - 2,...,\max{(1,i + 1 - k)}]$$$.
He wants to know the maximum streak of problem-solving he has in this month. Can you find it for him?
The maximum problem-solving streak means the maximum number of consecutive days where Monke has solved at least one problem each day.
For example, let $$$n = 5,\ k = 2$$$, and the number of problems he solved on the day $$$i$$$ is represented by the array $$$[1, 1, 0, 4, 1]$$$, then the array containing total solve count of last $$$\min(i,\ k)$$$ days will be $$$[1, 2, 1, 4, 5]$$$, and the maximum problem-solving streak will be $$$2$$$ days.
The input consists of multiple test cases. The first line contains an integer $$$t\ (1 \le t \le 10^4)$$$ — the number of test cases. The description of the test cases follows.
The first line of each test case contains two integers $$$n , k\ (2 \le n \le 3\cdot10^5, 1 \le k \le n)$$$ — the number of days in a month.
The second line of each test case contains $$$n$$$ integers $$$a_1,a_2, ... ,a_n\ (0 \le a_i \le 10 ^ 9)$$$ — the elements of $$$a$$$.
It is guaranteed that each $$$a_i$$$ $$$(1 \le i \le n)$$$ is consistent with all previous $$$a_j$$$ $$$(\max(1,\ i - k) \le j \le i - 1)$$$. In other words, the given solve count is valid.
It is guaranteed that the sum of $$$n$$$ across all test cases does not exceed $$$3\cdot10^5$$$.
For each test case, print one integer, the maximum problem-solving streak.
3 2 2 1 2 5 2 1 2 1 4 5 5 2 1 2 2 2 2
2 2 5
