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 Perl (v5.18.2) (judge verdict: Accepted)

#!/usr/bin/perl
my ($n,$k) = map { $_ - 0 } split(/\s+/,<STDIN>);
my $s = <STDIN>;

my $hn = 0;
my $g = 0;

my $c2 = substr($s,0,1);
for(my $i=0;$i<$n-1;$i++){
  my $c1 = $c2;
  $c2 = substr($s,$i+1,1);
  $hn ++ if $c1 eq $c2;
  $g ++ if $c1 ne $c2;
}

my $maxh = $hn;
if( $k * 2 <= $g ){
  $maxh += $k * 2;
} else {
  $maxh = $n - 1;
}
print "$maxh\n";

exit(0);