2^Sort

给你一个长度为 $n \ (\sum n < 2\cdot 10^5)$ 的数组 $a$，问你在这个数组中，有多少个长度为 $k + 1 \ (1\le k < n)$ 的区间，符合以下的条件： $$ 2^0 \cdot a_i < 2^1 \cdot a_{i + 1} < 2^2 \cdot a_{i + 2} < \dotsi < 2^k \cdot a_{i + k}\\ \footnotesize{注：i 为这个区间开始的位置} $$ 由[tzyt](https://www.luogu.com.cn/user/394488)翻译

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. More formally, count the number of indices $ 1 \leq i \leq n - k $ such that $ $$$2^0 \cdot a_i < 2^1 \cdot a_{i+1} < 2^2 \cdot a_{i+2} < \dots < 2^k \cdot a_{i+k}. $ $$$

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.

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

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 $ . In the second test case, three subarrays satisfy the condition: - $ 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.