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: Runtime Error)

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


def counthappy(s):
    happy = 0
    for i in range(0, len(s)):
        if i != 0 and s[i] == 'L':
            if s[i - 1] == 'L':
                happy += 1
        elif i != len(s) - 1 and s[i] == 'R':
            if s[i + 1] == 'R':
                happy += 1
    return happy


def replace(s, k_):
    for l in range(0, N - 1):
        for r in range(l + 1, N):
            part_l = s[0:l]
            part = s[l:r+1]
            part_r = s[r+1:N][::-1]

            part = part.replace('L', '-')
            part = part.replace('R', 'L')
            part = part.replace('-', 'R')
            s_ = part_l + part + part_r

            if k_ < K:
                replace(s_, k_ + 1)

            happy = counthappy(s_)
            global answer
            if answer < happy:
                answer = happy


answer = counthappy(S)
replace(S, 1)

print(answer)