2^Sort
Description
Given an array $a$ of length $n$ and an integer $k$, find the number of indices $1 \leq i \leq n - k$ such that the subarray $[a_i, \dots, a_{i+k}]$ with length $k+1$ (not with length $k$) has the following property:
- If you multiply the first element by $2^0$, the second element by $2^1$, ..., and the ($k+1$)-st element by $2^k$, then this subarray is sorted in strictly increasing order.
The first line contains an integer $t$ ($1 \leq t \leq 1000$) — the number of test cases.
The first line of each test case contains two integers $n$, $k$ ($3 \leq n \leq 2 \cdot 10^5$, $1 \leq k < n$) — the length of the array and the number of inequalities.
The second line of each test case contains $n$ integers $a_1, a_2, \dots, a_n$ ($1 \leq a_i \leq 10^9$) — the elements of the array.
The sum of $n$ across all test cases does not exceed $2 \cdot 10^5$.
For each test case, output a single integer — the number of indices satisfying the condition in the statement.
Input
The first line contains an integer $t$ ($1 \leq t \leq 1000$) — the number of test cases.
The first line of each test case contains two integers $n$, $k$ ($3 \leq n \leq 2 \cdot 10^5$, $1 \leq k < n$) — the length of the array and the number of inequalities.
The second line of each test case contains $n$ integers $a_1, a_2, \dots, a_n$ ($1 \leq a_i \leq 10^9$) — the elements of the array.
The sum of $n$ across all test cases does not exceed $2 \cdot 10^5$.
Output
For each test case, output a single integer — the number of indices satisfying the condition in the statement.
Samples
6
4 2
20 22 19 84
5 1
9 5 3 2 1
5 2
9 5 3 2 1
7 2
22 12 16 4 3 22 12
7 3
22 12 16 4 3 22 12
9 3
3 9 12 3 9 12 3 9 12
2
3
2
3
1
0
Note
In the first test case, both subarrays satisfy the condition:
- $i=1$: the subarray $[a_1,a_2,a_3] = [20,22,19]$, and $1 \cdot 20 < 2 \cdot 22 < 4 \cdot 19$.
- $i=2$: the subarray $[a_2,a_3,a_4] = [22,19,84]$, and $1 \cdot 22 < 2 \cdot 19 < 4 \cdot 84$.
- $i=1$: the subarray $[a_1,a_2] = [9,5]$, and $1 \cdot 9 < 2 \cdot 5$.
- $i=2$: the subarray $[a_2,a_3] = [5,3]$, and $1 \cdot 5 < 2 \cdot 3$.
- $i=3$: the subarray $[a_3,a_4] = [3,2]$, and $1 \cdot 3 < 2 \cdot 2$.
- $i=4$: the subarray $[a_4,a_5] = [2,1]$, but $1 \cdot 2 = 2 \cdot 1$, so this subarray doesn't satisfy the condition.