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 PHP7 (7.0.15) (judge verdict: Runtime Error)

<?php                                                                                                                                                                                                                                                                                                                          
                                                                                                                                                                                                                                                                                                                               
function fget_array() {                                                                                                                                                                                                                                                                                                        
    return explode(' ', trim(fgets(STDIN)));                                                                                                                                                                                                                                                                                   
}                                                                                                                                                                                                                                                                                                                              
                                                                                                                                                                                                                                                                                                                               
[$n, $k] = fget_array();                                                                                                                                                                                                                                                                                                       
$str = fget_array()[0];                                                                                                                                                                                                                                                                                                        
$count = [];                                                                                                                                                                                                                                                                                                                   
for ($i = 1, $j = 0; $i <= $n; $i++) {                                                                                                                                                                                                                                                                                         
    $s = $str[$i] ?? null;                                                                                                                                                                                                                                                                                                     
    $prev = $str[$i - 1];                                                                                                                                                                                                                                                                                                      
    if ($prev === $s) {                                                                                                                                                                                                                                                                                                        
        $j++;                                                                                                                                                                                                                                                                                                                  
    } else {                                                                                                                                                                                                                                                                                                                   
        $count[] = $j;                                                                                                                                                                                                                                                                                                         
        $j = 0;                                                                                                                                                                                                                                                                                                                
    }                                                                                                                                                                                                                                                                                                                          
    $prev = $s;                                                                                                                                                                                                                                                                                                                
}                                                                                                                                                                                                                                                                                                                              
                                                                                                                                                                                                                                                                                                                               
$limit = count($count) - 1;                                                                                                                                                                                                                                                                                                    
$list = [];                                                                                                                                                                                                                                                                                                                    
foreach ($count as $key => $v) {                                                                                                                                                                                                                                                                                               
    $plus = in_array($key, [0, $limit]) ? 2 : 3;                                                                                                                                                                                                                                                                               
    $list[$v+1][] = $v + $plus;                                                                                                                                                                                                                                                                                                
}                                                                                                                                                                                                                                                                                                                              
                                                                                                                                                                                                                                                                                                                               
$result = 0;                                                                                                                                                                                                                                                                                                                   
$j = 0;                                                                                                                                                                                                                                                                                                                        
for ($i = 1; $j <= $k; $i++) {                                                                                                                                                                                                                                                                                                 
    $a = $list[$i] ?? [];                                                                                                                                                                                                                                                                                                      
    rsort($a);                                                                                                                                                                                                                                                                                                                 
    foreach ($a as $v) {                                                                                                                                                                                                                                                                                                       
        $j += $i;                                                                                                                                                                                                                                                                                                              
        $result += $v - $i;                                                                                                                                                                                                                                                                                                    
        if ($j < $k) continue;                                                                                                                                                                                                                                                                                                 
        break;                                                                                                                                                                                                                                                                                                                 
    }                                                                                                                                                                                                                                                                                                                          
    if ($j < $k) continue;                                                                                                                                                                                                                                                                                                     
    break;                                                                                                                                                                                                                                                                                                                     
}                                                                                                                                                                                                                                                                                                                              
echo $result + array_sum($count);                                                                                                                                                                                                                                                                                              
?>