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: Wrong Answer)

fun main(args: Array<String>) {
    val (N, K) = readInputLine().split(" ").map { it.toInt() }
    val S = readInputLine().toCharArray()

    val dims = mutableListOf<Pair<Int, Int>>()
    
    var now = S[0]
    var start = 0
    
    for (i in 1 until N) {
        if (S[i] != now) {
            dims.add(Pair(start, i - 1))
            now = S[i]
            start = i
        }
    }
    
    dims.add(Pair(start, N - 1))
    
    for (i in 1..K) {
        if (dims.size == 1) {
            break
        } else if (dims.size == 2) {
            val a = dims.removeAt(0)
            val b = dims.removeAt(0)

            dims.add(Pair(a.first, b.second))
        } else {
            val a = dims.removeAt(0)
            val b = dims.removeAt(0)
            val c = dims.removeAt(0)
            
            dims.add(Pair(a.first, c.second))
        }
    }

    println(dims.sumBy { it.second - it.first})
}

fun readInputLine(): String {
    return readLine()!!
}