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 (1.15.1) (judge verdict: Accepted)

use std::cmp::*;

#[allow(dead_code)]
fn read<T: std::str::FromStr>() -> T {
    use std::io::Read;
    let token: String = std::io::stdin()
        .bytes()
        .map(|c| c.unwrap() as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().unwrap()
}

#[allow(dead_code)]
fn read_line<T: std::str::FromStr>() -> T {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().parse().ok().unwrap()
}

#[allow(non_snake_case)]
fn main() {
    let N: u32 = read();
    let mut K: usize = read();
    let S: String = read_line();
    let mut cnt1: Vec<u32> = Vec::new();
    let mut cnt0: Vec<u32> = Vec::new();
    let mut chars = S.chars();
    let mut tmp_b: bool = true;
    let mut tmp_cnt = 0u32;
    for c in chars {
        if c as u8 - 48 == tmp_b as u8 {
            tmp_cnt += 1;
        } else {
            if tmp_b {
                cnt1.push(tmp_cnt);
            } else {
                cnt0.push(tmp_cnt);
            }
            tmp_cnt = 1;
            tmp_b = !tmp_b;
        }
    }
    if tmp_b {
        cnt1.push(tmp_cnt);
    } else {
        cnt0.push(tmp_cnt);
    }
    if cnt1.len() == cnt0.len() {
        cnt1.push(0);
    }
    let mut acc1 = vec![0u32; cnt1.len()+1];
    let mut acc0 = vec![0u32; cnt0.len()+1];
    acc1[0] = 0;
    acc0[0] = 0;
    for i in 0..cnt1.len() {
        acc1[i+1] = acc1[i] + cnt1[i];
    }
    for i in 0..cnt0.len() {
        acc0[i+1] = acc0[i] + cnt0[i];
    }

    K = min(K, cnt0.len());
    let mut ans = 0u32;
    for i in 0..cnt0.len()-K+1 {
        ans = max(ans, acc1[i+K+1]-acc1[i]+acc0[i+K]-acc0[i]);
    }

    println!("{}", ans);
}