You are given a number $k$ and a string $s$ of length $n$, consisting of the characters '.' and '\*'. You want to replace some of the '\*' characters with 'x' characters so that the following conditions are met:

• The first character '\*' in the original string should be replaced with 'x';
• The last character '\*' in the original string should be replaced with 'x';
• The distance between two neighboring replaced characters 'x' must not exceed $k$ (more formally, if you replaced characters at positions $i$ and $j$ ($i \lt j$) and at positions $[i+1, j-1]$ there is no "x" symbol, then $j-i$ must be no more than $k$).

For example, if $n=7$, $s=$.\*\*.\*\*\* and $k=3$, then the following strings will satisfy the conditions above:

• .xx.\*xx;
• .x\*.x\*x;
• .xx.xxx.

But, for example, the following strings will not meet the conditions:

• .\*\*.\*xx (the first character '\*' should be replaced with 'x');
• .x\*.xx\* (the last character '\*' should be replaced with 'x');
• .x\*.\*xx (the distance between characters at positions $2$ and $6$ is greater than $k=3$).

Given $n$, $k$, and $s$, find the minimum number of '\*' characters that must be replaced with 'x' in order to meet the above conditions.

Input

The first line contains one integer $t$ ($1 \le t \le 500$). Then $t$ test cases follow.

The first line of each test case contains two integers $n$ and $k$ ($1 \le k \le n \le 50$).

The second line of each test case contains a string $s$ of length $n$, consisting of the characters '.' and '\*'.

It is guaranteed that there is at least one '\*' in the string $s$.

It is guaranteed that the distance between any two neighboring '\*' characters does not exceed $k$.

Output

For each test case output the minimum number of '\*' characters that must be replaced with 'x' characters in order to satisfy the conditions above.

Samples

5
7 3
.**.***
5 1
..*..
5 2
*.*.*
3 2
*.*
1 1
*

3
1
3
2
1