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

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 $$$n$$$, $$$k$$$ ($$$3 \leq n \leq 2 \cdot 10^5$$$, $$$1 \leq k \lt n$$$) — 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.

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 $$$1 \cdot 20 \lt 2 \cdot 22 \lt 4 \cdot 19$$$.
$$$i=2$$$: the subarray $$$[a_2,a_3,a_4] = [22,19,84]$$$, and $$$1 \cdot 22 \lt 2 \cdot 19 \lt 4 \cdot 84$$$.

In the second test case, three subarrays satisfy the condition:

$$$i=1$$$: the subarray $$$[a_1,a_2] = [9,5]$$$, and $$$1 \cdot 9 \lt 2 \cdot 5$$$.
$$$i=2$$$: the subarray $$$[a_2,a_3] = [5,3]$$$, and $$$1 \cdot 5 \lt 2 \cdot 3$$$.
$$$i=3$$$: the subarray $$$[a_3,a_4] = [3,2]$$$, and $$$1 \cdot 3 \lt 2 \cdot 2$$$.
$$$i=4$$$: the subarray $$$[a_4,a_5] = [2,1]$$$, but $$$1 \cdot 2 = 2 \cdot 1$$$, so this subarray doesn't satisfy the condition.

2^Sort

Examples