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::stdin;

fn main() {
    let mut nk = String::new();
    stdin().read_line(&mut nk).unwrap();
    let nk: Vec<usize> = nk.trim().split_whitespace().flat_map(str::parse).collect();
    let mut s = String::new();
    stdin().read_line(&mut s).unwrap();

    let (n, k) = (nk[0], nk[1]);
    let s = s.trim();
    let mut start = None;
    let mut ps = Vec::new();
    let mut ss: Vec<_> = s.chars().collect();
    ss.push('1');
    for i in 0..n + 1 {
        match ss[i] {
            '0' if start == None => {
                start = Some(i);
            }
            '1' if start != None => {
                ps.push((start.unwrap(), i));
                start = None;
            }
            _ => {}
        }
    }

    let mut result = None;
    for i in 0..if ps.len() as isize - k as isize + 1 <= 0 { 1 } else { ps.len() - k + 1 } {
        let start = if i > 0 { ps[i - 1].1 } else { 0 };
        let end = if i + k < ps.len() { ps[i + k].0 } else { n };
        if result == None || result < Some(end - start) {
            result = Some(end - start);
        }
    }
    println!("{}", result.unwrap());
}