D - Face Produces Unhappiness /

問題文

どの人も、目の前の人が自分と同じ方向を向いていれば幸福です。 ただし、目の前に人が居ない場合、幸福ではありません。

あなたは、以下の操作を 0 回以上 K 回以下の好きな回数だけ行います。

制約

• N1 \leq N \leq 10^5 を満たす整数である。
• K1 \leq K \leq 10^5 を満たす整数である。
• |S| = N
• S の各文字は L または R である。

入力

N K
S


出力

K 回以下の操作後に幸福である人数の最大値を出力せよ。

入力例 1

6 1
LRLRRL


出力例 1

3


(l, r) = (2, 5) と選べば LLLRLL となり、西から 2, 3, 6 番目の人が幸福です。

入力例 2

13 3
LRRLRLRRLRLLR


出力例 2

9


入力例 3

10 1
LLLLLRRRRR


出力例 3

9


入力例 4

9 2
RRRLRLRLL


出力例 4

7


Score : 400 points

Problem Statement

There are N people standing in a queue from west to east.

Given is a string S of length N representing the directions of the people. The i-th person from the west is facing west if the i-th character of S is L, and east if that character of S is R.

A person is happy if the person in front of him/her is facing the same direction. If no person is standing in front of a person, however, he/she is not happy.

You can perform the following operation any number of times between 0 and K (inclusive):

Operation: Choose integers l and r such that 1 \leq l \leq r \leq N, and rotate by 180 degrees the part of the queue: the l-th, (l+1)-th, ..., r-th persons. That is, for each i = 0, 1, ..., r-l, the (l + i)-th person from the west will stand the (r - i)-th from the west after the operation, facing east if he/she is facing west now, and vice versa.

What is the maximum possible number of happy people you can have?

Constraints

• N is an integer satisfying 1 \leq N \leq 10^5.
• K is an integer satisfying 1 \leq K \leq 10^5.
• |S| = N
• Each character of S is L or R.

Input

Input is given from Standard Input in the following format:

N K
S


Output

Print the maximum possible number of happy people after at most K operations.

Sample Input 1

6 1
LRLRRL


Sample Output 1

3


If we choose (l, r) = (2, 5), we have LLLRLL, where the 2-nd, 3-rd, and 6-th persons from the west are happy.

Sample Input 2

13 3
LRRLRLRRLRLLR


Sample Output 2

9


Sample Input 3

10 1
LLLLLRRRRR


Sample Output 3

9


Sample Input 4

9 2
RRRLRLRLL


Sample Output 4

7