Face Produces Unhappiness

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.

Examples

Input

6 1 LRLRRL

Output

3

Input

13 3 LRRLRLRRLRLLR

Output

9

Input

10 1 LLLLLRRRRR

Output

9

Input

9 2 RRRLRLRLL

Output

7

inputFormat

Input

Input is given from Standard Input in the following format:

N K S

outputFormat

Output

Print the maximum possible number of happy people after at most K operations.

Examples

Input

6 1 LRLRRL

Output

3

Input

13 3 LRRLRLRRLRLLR

Output

9

Input

10 1 LLLLLRRRRR

Output

9

Input

9 2 RRRLRLRLL

Output

7

样例

6 1
LRLRRL

3