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::str::FromStr;
use std::fmt::Debug;
use std::cmp;

fn read_as_vec<T>() -> Vec<T>
where T: FromStr, <T as FromStr>::Err : Debug{
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).unwrap();
    s.trim().split_whitespace().map(|c| T::from_str(c).unwrap()).collect()

}

fn read_as_string() -> String{
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).unwrap();
    s.trim().to_string()
}

fn main(){
    let line: Vec<usize> = read_as_vec();
    //let (n, k) = (line[0], line[1]);
    let n = line[0];
    let mut k = line[1];

    let people = read_as_string();
    let people: Vec<char> = people.chars().collect();
    
    //println!("{:?}",people);

    //find the longest handstanding line

    let (mut i, mut j) = (0, 0);
    while j < n{
        while j < n && people[j] == '1'{
            j += 1;
        }

        if k > 0{
            k -= 1;
        }else{
            break;
        }
        
        while j < n && people[j] == '0'{
            j += 1;
        }
    }
    if j == n{
        println!("{}", j-i);
        return;
    }
    let mut longest : (usize, usize)= (i, j);
    /*
    println!("i = {}, j = {}", i, j);
    println!("k = {}", k);
    */
    loop{   
        while people[i] == '1' && i <=j{
            i += 1;
        }

        k += 1;
        while people[i] == '0' && i <= j{
            i += 1;
        }

        k -= 1;
        while j < n && people[j] == '0'{
            j += 1;
        }
        while j < n && people[j] == '1'{
            j += 1;
        }



        
        if longest.1-longest.0 < j-i{
            longest = (i, j);
        }
        if j >= n{
            break;
        }
    }

    /*
    println!("i = {}, j = {}", i, j);
    println!("k = {}", k);
    */
    println!("{:?}", longest.1-longest.0);
}