B. Partial Replacement
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

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 $j$ ($i < j$) 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.

Example
Input
5
7 3
.**.***
5 1
..*..
5 2
*.*.*
3 2
*.*
1 1
*

Output
3
1
3
2
1