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 C (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <stdio.h>

char s[500001];

int main(void)
{
    unsigned int n, k;
    unsigned int i;
    unsigned int ret = 0;
    unsigned int cross = 0;
    unsigned int haji = 0;

    scanf("%d %d", &n, &k);
    scanf("%s", s);

    if ((s[0] == 'L') && (s[n - 1] == 'R')) haji++;

    for (i = 0; i < (n - 1); i++) {
        if (s[i] == s[i + 1]) {
            ret++;
        } else if ((s[i] == 'R') && (s[i + 1] == 'L')) {
            cross++;
        }
    }
    while ((k > 0) && ((cross > 0) || (haji > 0))) {
        if (cross > 1) {
            cross--;
            ret += 2; 
        } else if (cross > 0) {
            cross--;
            ret++;
        } else if (haji > 0) {
            haji--;
            ret++;
        }
        k--;
    }
    
    printf("%d", ret);

    return 0;
}