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::max;
use std::io::prelude::*;
use std::io::stdin;
use std::str::FromStr;

fn main() {
    let n: usize = read();
    let k: usize = read();
    let s: Vec<char> = read::<String>().chars().collect();

    let mut cnt = 1;
    let mut cnts = vec![];
    let mut uprights = 0;

    for i in 0..n - 1 {
        if s[i] != s[i + 1] {
            if cnt != 0 {
                if s[i] == '0' {
                    uprights += 1;
                }
                cnts.push(cnt);
                cnt = 0;
            }
        }
        cnt += 1;
    }
    if cnt != 0 {
        cnts.push(cnt);
    }
    if s[n - 1] == '0' {
        uprights += 1;
    }

    if uprights <= k {
        println!("{}", n);
        return;
    }

    let mut max_i = 0;

    if s[0] == '0' {
        max_i = max(max_i, cnts.iter().take(2 * k).sum());
        cnts.remove(0);
    }

    if s[n - 1] == '0' {
        max_i = max(max_i, cnts.iter().rev().take(2 * k).sum());
        let last = cnts.len() - 1;
        cnts.remove(last);
    }

    if cnts.len() > 2 * k {
        let mut v = vec![0; cnts.len() + 1];

        for i in 0..cnts.len() {
            v[i + 1] = v[i] + cnts[i];
        }

        for (i, j) in (2 * k + 1..v.len()).enumerate() {
            if i % 2 == 0 {
                max_i = max(max_i, v[j] - v[j - (2 * k + 1)]);
            }
        }
    }

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

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