Problem:
Score : 400 points

Problem Statement

N people are arranged in a row from left to right.

You are given a string S of length N consisting of 0 and 1, and a positive integer K.

The i-th person from the left is standing on feet if the i-th character of S is 0, and standing on hands if that character is 1.

You will give the following direction at most K times (possibly zero):

Direction: Choose integers l and r satisfying 1 \leq l \leq r \leq N, and flip the l-th, (l+1)-th, ..., and r-th persons. That is, for each i = l, l+1, ..., r, the i-th person from the left now stands on hands if he/she was standing on feet, and stands on feet if he/she was standing on hands.

Find the maximum possible number of consecutive people standing on hands after at most K directions.

Constraints

N is an integer satisfying 1 \leq N \leq 10^5.

K is an integer satisfying 1 \leq K \leq 10^5.

The length of the string S is N.

Each character of the string S is 0 or 1.

Input

Input is given from Standard Input in the following format:

N K
S

Output

Print the maximum possible number of consecutive people standing on hands after at most K directions.

Sample Input 1

5 1
00010

Sample Output 1

4

We can have four consecutive people standing on hands, which is the maximum result, by giving the following direction:

Give the direction with l = 1, r = 3, which flips the first, second and third persons from the left.

Sample Input 2

14 2
11101010110011

Sample Output 2

8

Sample Input 3

1 1
1

Sample Output 3

1

No directions are necessary.

Solution in Rust (1.42.0) (judge verdict: Accepted)

use proconio::input;
use proconio::marker::Chars;

#[derive(Debug)]
enum State {
    Upright(usize),
    Handstand(usize),
}

fn main() {
    input! {
        _n: usize,
        k: usize,
        s: Chars,
    }

    let mut seq = vec![];

    for c in s {
        match c {
            '0' => {
                if let Some(State::Upright(n)) = seq.last_mut() {
                    *n += 1;
                } else {
                    seq.push(State::Upright(1));
                }
            },
            '1' => {
                if let Some(State::Handstand(n)) = seq.last_mut() {
                    *n += 1;
                } else {
                    seq.push(State::Handstand(1));
                }
            }
            _ => {},
        }
    }

    let mut max_length: usize = 0;
    let mut first_index = None;
    let mut count = 0;
    let mut current_length = 0;
    for i in 0..seq.len() {
        match seq[i] {
            State::Handstand(n) => {
                current_length += n;
            },
            State::Upright(n) => {
                if first_index.is_none() {
                    first_index = Some(i);
                }
                count += 1;
                if count > k {
                    if let Some(index) = first_index.as_mut() {
                        if let State::Upright(num) = seq[*index] {
                            current_length -= num;
                        }
                        if *index > 0 {
                            if let State::Handstand(num) = seq[*index - 1] {
                                current_length -= num;
                            }
                        }
                        *index += 2;
                    }
                }
                current_length += n;
            }
        }
        max_length = std::cmp::max(max_length, current_length);
    }
    println!("{}", max_length);
}