Partial Replacement

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.

• .**.*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.