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::io::*;
use std::str::FromStr;
use std::cmp::{min, max};

pub fn read<T: FromStr>() -> T {
    let stdin = stdin();
    let stdin = stdin.lock();
    let token: String = stdin
        .bytes()
        .map(|c| c.expect("failed reading char") as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().expect("failed parsing")
}

fn main() {
    let N:usize = read();
    let K:usize = read();
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s = s.trim_right().to_owned();
    let b :Vec<i32> = s.into_bytes().iter().map(|&x| x as i32 - '0' as i32).collect();
    let mut c:Vec<i32> = Vec::new();
    let mut temp = 1;
    for i in 0..N-1 {
        let i = i as usize;
        if b[i]!=b[i+1]{
            c.push(temp);
            temp = 0;
        }
        temp = temp+1;
    }
    c.push(temp);
//    println!("{:?}",c);

    let clen = c.len();
    let mut sumvec:Vec<i32> = vec![0];
    for i in 0..clen{
        let temp = sumvec[i];
        sumvec.push(temp+c[i]);
    }

    sumvec.push(N as i32);
    sumvec.push(N as i32);
    sumvec.push(N as i32);
    sumvec.push(N as i32);

//    println!("{:?}",sumvec);

    let flag:bool = b[0]==1;

    //0スタート : 2K個

    let mut ans = 0;

    if !flag {
        let left:usize = 0;
        let right:usize = min(left+2*K,clen);
        ans = sumvec[right]-sumvec[left];
    }

    //1スタート : 2K+1個
    let mut left = if flag{0}else{1};
    let mut right = min(left+2*K+1,clen);
    left = min(clen,left);
    while right <= clen+1 {
//        println!("[1]left:{}, right:{}, sum:{}",left,right,ans);
        ans = max(sumvec[right]-sumvec[left],ans);
        left = left+2;
        right = right+2;
    }
//    println!("[1]left:{}, right:{}, sum:{}",left,right,ans);

    println!("{}",ans);

}