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 Rust (1.42.0) (judge verdict: Accepted)

#![allow(unused_attributes)]
///   _           _                    __
///  | |         | |                  / /
///  | |__   __ _| |_ ___   ___      / /
///  | '_ \ / _` | __/ _ \ / _ \    / /
///  | | | | (_| | || (_) | (_) |  / /   _ _   _                                 _                    _                  _
///  |_| |_|\__,_|\__\___/ \___/  /_/ | (_) | (_)                               | |                  (_)                | |
///    ___ ___  _ __ ___  _ __   ___| |_ _| |_ ___   _____ ______ _ __ _   _ ___| |_ ______ ___ _ __  _ _ __  _ __   ___| |_ ___
///   / __/ _ \| '_ ` _ \| '_ \ / _ \ __| | __| \ \ / / _ \______| '__| | | / __| __|______/ __| '_ \| | '_ \| '_ \ / _ \ __/ __|
///  | (_| (_) | | | | | | |_) |  __/ |_| | |_| |\ V /  __/      | |  | |_| \__ \ |_       \__ \ | | | | |_) | |_) |  __/ |_\__ \
///   \___\___/|_| |_| |_| .__/ \___|\__|_|\__|_| \_/ \___|      |_|   \__,_|___/\__|      |___/_| |_|_| .__/| .__/ \___|\__|___/
///                      | |                                                                           | |   | |
///                      |_|                                                                           |_|   |_|
/// https://github.com/hatoo/competitive-rust-snippets
#[allow(unused_imports)]
use std::cmp::{max, min, Ordering, Reverse};
#[allow(unused_imports)]
use std::collections::{BTreeMap, BTreeSet, BinaryHeap, HashMap, HashSet, VecDeque};
#[allow(unused_imports)]
use std::io::{stdin, stdout, BufWriter, Write};
#[allow(unused_imports)]
use std::iter::FromIterator;
mod util {
    use std::fmt::Debug;
    use std::io::{stdin, stdout, BufWriter, StdoutLock};
    use std::str::FromStr;
    #[allow(dead_code)]
    pub fn line() -> String {
        let mut line: String = String::new();
        stdin().read_line(&mut line).unwrap();
        line.trim().to_string()
    }
    #[allow(dead_code)]
    pub fn chars() -> Vec<char> {
        line().chars().collect()
    }
    #[allow(dead_code)]
    pub fn gets<T: FromStr>() -> Vec<T>
    where
        <T as FromStr>::Err: Debug,
    {
        let mut line: String = String::new();
        stdin().read_line(&mut line).unwrap();
        line.split_whitespace()
            .map(|t| t.parse().unwrap())
            .collect()
    }
    #[allow(dead_code)]
    pub fn with_bufwriter<F: FnOnce(BufWriter<StdoutLock>)>(f: F) {
        let out = stdout();
        let writer = BufWriter::new(out.lock());
        f(writer)
    }
}
#[allow(unused_macros)]
macro_rules ! get {([$ t : ty ] ) => {{let mut line : String = String :: new () ; stdin () . read_line (& mut line ) . unwrap () ; line . split_whitespace () . map (| t | t . parse ::<$ t > () . unwrap () ) . collect ::< Vec < _ >> () } } ; ([$ t : ty ] ; $ n : expr ) => {(0 ..$ n ) . map (| _ | get ! ([$ t ] ) ) . collect ::< Vec < _ >> () } ; ($ t : ty ) => {{let mut line : String = String :: new () ; stdin () . read_line (& mut line ) . unwrap () ; line . trim () . parse ::<$ t > () . unwrap () } } ; ($ ($ t : ty ) ,* ) => {{let mut line : String = String :: new () ; stdin () . read_line (& mut line ) . unwrap () ; let mut iter = line . split_whitespace () ; ($ (iter . next () . unwrap () . parse ::<$ t > () . unwrap () , ) * ) } } ; ($ t : ty ; $ n : expr ) => {(0 ..$ n ) . map (| _ | get ! ($ t ) ) . collect ::< Vec < _ >> () } ; ($ ($ t : ty ) ,*; $ n : expr ) => {(0 ..$ n ) . map (| _ | get ! ($ ($ t ) ,* ) ) . collect ::< Vec < _ >> () } ; }
const BIG_STACK_SIZE: bool = true;
#[allow(dead_code)]
fn main() {
    use std::thread;
    if BIG_STACK_SIZE {
        thread::Builder::new()
            .stack_size(32 * 1024 * 1024)
            .name("solve".into())
            .spawn(solve)
            .unwrap()
            .join()
            .unwrap();
    } else {
        solve();
    }
}
fn solve() {
    let (_n, k) = get!(usize, usize);
    let lr = get!(String);

    let mut arr: Vec<u64> = Vec::new();
    
    {
        let mut prev = false;
        let mut t = 0;
        for c in lr.chars() {
            let l = c == 'L';
            if prev != l {
                if t!=0 {
                    arr.push(t);
                }
                t = 0;
            }
            t += 1;
            prev = l;
        }
        if t!=0 {
            arr.push(t);
        }
    }

    for _ in 0..k {
        if arr.len() >= 3 {
            let a = arr.pop().unwrap();
            let b = arr.pop().unwrap();
            let c = arr.pop().unwrap();
            arr.push(a+b+c);
        } else {
            arr = vec![arr.iter().sum::<u64>()];
        }
    }

    println!("{}", arr.iter().sum::<u64>() - arr.len() as u64);
}