Problem:
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

Solution in Python (3.4.3) (judge verdict: Wrong Answer)

import sys

N, K = map(int, input().split())
S = list(input())

shiawase = 0
# 幸せカウント
for i in range(N-1):
    if S[i] == S[i+1]:
        shiawase += 1


if N == 1:
    print(0)
    sys.exit(0)

# N >= 2
left = 0
right = N-2

count = [0, 0]
hanten = 0

# for i in range(K + 2):
while K > 0:
    # left, right をすすめる
    while left < N-1 and S[left] == S[left+1]:
        left += 1
        if S[left] == "L":
            count[hanten] += 1
        else:
            count[1 - hanten] += 1
    while right >= 0 and S[right] == S[right+1]:
        right -= 1
        if S[left] == "R":
            count[hanten] += 1
        else:
            count[1 - hanten] += 1

    if left >= right:
        break

    shiawase += 2

    K -= 1
    hanten = 1 - hanten

shiawase += min(K, *count)


print(shiawase)