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 Kotlin (1.0.0) (judge verdict: Runtime Error)

fun main(args: Array<String>) {
    val (n, k) = readLine()!!.split(" ").map { it.toInt() }
    val s = readLine()!!

    // どういう順番でどこを回すのが最適か？？

    // 毎回回転後のスコアが最大となる部分を回す？
    // 中心箇所の選択 & 範囲の選択, 奇数・偶数個？
    // -> 10^5パターン & 10^5パターン になって x

    // 180度回転の内部ではスコアは変わらない
    // 変わるのは境界部分の関係性(スコア）

    // 2点変わることろから変えていくのがベスト

    var sum = 0
    var prev = 'N'
    var next = 'N'
    var score = mutableListOf<Int>()
    for ( i in 0 until s.length ) {

        prev = if(i-1 < 0) 'N' else s[i-1]
        next = if(i+1 > s.length-1) 'N' else s[i+1]

        if(s[i] == next) {
            sum+=1
        }

        if ( prev == s[i] && next == s[i]) {
            score.add(-2)

        } else if((prev == s[i] && next != s[i]) || (prev != s[i] && next == s[i])) {
            if (prev == 'N' || next == 'N'){
                score.add(1)
            } else {
                score.add(0)
            }
        } else if ( prev != s[i] && next != s[i] ) {
            score.add(2)
        }
    }

    score.sortDescending()

    for ( i in 0 until k) {
        if( score[i] == 0) {
            break
        }
        sum += score[i]

    }

    println(sum)

}