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: Time Limit Exceeded)

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

l = -1
r = -1

for k in range(K):
    for i in range(1, N):
        if S[i] != S[i-1]:
            if l < 0:
                l = i
            else:
                r = i
                for s in range(l, r):
                    if S[s] == "L":
                        S[s] = "R"
                    else:
                        S[s] = "L"
                l = -1
                r = -1
                break
        elif i == N-1 and l >= 0:
            for s in range(l, N):
                if S[s] == "L":
                    S[s] = "R"
                else:
                    S[s] = "L"
            l = -1
            break
ans = 0
for i in range(1, N):
    if S[i] == S[i-1]:
        ans += 1

print(ans)