
Score : 400 points
Problem StatementThere 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.
InputInput is given from Standard Input in the following format:
N K
S
OutputPrint the maximum possible number of happy people after at most K operations.
Sample Input 16 1
LRLRRL
Sample Output 13
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 213 3
LRRLRLRRLRLLR
Sample Output 29
Sample Input 310 1
LLLLLRRRRR
Sample Output 39
Sample Input 49 2
RRRLRLRLL
Sample Output 47
