G. 2^Sort
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

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 $$$$$$2^0 \cdot a_i < 2^1 \cdot a_{i+1} < 2^2 \cdot a_{i+2} < \dots < 2^k \cdot a_{i+k}.$$$$$$
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.

Example
Input
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
Output
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 $$$1 \cdot 22 < 2 \cdot 19 < 4 \cdot 84$$$.
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.