Canadian Computing Competition: 2009 Stage 2, Day 1, Problem 2

On the way to dinner, the CCC competitors are lining up for their delicious curly fries. The $N$ $(1\le N\le 100)$ competitors have lined up single-file to enter the cafeteria.

Doctor V, who runs the CCC, realized at the last minute that programmers simply hate standing in line next to programmers who use a different language. Thankfully, only two languages are allowed at the CCC: Gnold and Helpfile. Furthermore, the competitors have decided that they will only enter the cafeteria if they are in a group of at least $K$ $(1\le K\le 6)$ competitors.

Doctor V decided to iterate the following scheme:

• He will find a group of $K$ or more competitors who use the same language standing next to each other in line and send them to dinner.
• The remaining competitors will close the gap, potentially putting similar-language competitors together.

So Doctor V recorded the sequence of competitors for you. Can all the competitors dine? If so, what is the minimum number of groups of competitors to be sent to dinner?

Note: Test cases worth $60\mathrm{\%}$ of the points have $K\le 2$. Out of these, on test cases worth one third of the points ($20\mathrm{\%}$ of the total points), $N\le 10$.

Input Specification

The first line contains two integers $N$ and $K$.

The second line contains $N$ characters that are the sequence of competitors in line (H represents Helpfile, G represents Gnold)

Output Specification

Output, on one line, the single number that is the minimum number of groups that are formed for dinner. If not all programmers can dine, output -1.

Sample Input

7 2
GHHGHHG

Description of Sample Input

There are seven competitors: a Gnold programmer followed by two Helpfile programmers, followed by another Gnold programmer, followed by another two Helpfile programmers followed by a final Gnold programmer. Programmers want to go to dinner in pairs.

Output for Sample Input

3

Description of Output for Sample Input

First send the first pair of Hs to dinner, leaving GGHHG. Then send the second pair of Hs to dinner, leaving GGG; finally, send in the group of Gs. It might be coincidental that the two pairs of Helpfile programmers entered the cafeteria successively.