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;

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

fn skip(pos: usize, target: usize, seq: &Vec<usize>) -> usize {
    let n = seq.len();
    let mut prev = target;
    for i in pos..n {
        if prev != seq[i] && seq[i] == target {
            return i;
        }
        prev = seq[i];
    }
    return n;
}

fn main() {
    let n = read::<usize>();
    let k = read::<usize>();
    let seq = read::<String>()
        .chars()
        .map(|c| (c as u8 - '0' as u8) as usize)
        .collect::<Vec<usize>>();
    let mut r = 0;
    while r < n && seq[r] == 1 {
        r += 1;
    }
    for _ in 0..k {
        r = skip(r, 0, &seq);
    }
    let mut l = 0;
    let mut ans = r - l;
    for _ in 0..n {
        r = skip(r, 0, &seq);
        l = skip(l, 1, &seq);
        ans = std::cmp::max(ans, r - l);
    }
    println!("{}", ans);
}