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.

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

3
1
3
2
1