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 Python (3.4.3) (judge verdict: Time Limit Exceeded)

N,K=map(int,input().split())
S=list(input())

def happy(n):
	h=0
	for  i in range(len(n)-1):
		if n[i]==n[i+1]:
			h+=1

	return h

def cange(n,l,r):
	x=n[:l-1]
	y=n[r:]
	r=n[l-1:r]
	r.reverse()
	_R=[]
	for i in r:
		if i=="L":
			_R.append("R")
		else:
			_R.append("L")

	x.extend(_R)
	x.extend(y)
	return x

MAX=[0]
old=[happy(S),0,0]
for T in range(K):
	for l in range(1,N+1):
		for r in range(l,N+1):
			hpp=happy(cange(S,l,r))
			if hpp>=old[0]:
				old=[hpp,l,r]

	S=cange(S,old[1],old[2])

print(old[0])