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 (1.42.0) (judge verdict: Accepted)

use itertools::Itertools;
use proconio::input;
use proconio::marker::{Chars, Usize1};
use std::cmp::*;
use std::collections::*;
use std::iter::Iterator;

#[allow(unused_macros)]
macro_rules! max {
    ($x:expr) => {
      $x
    };
    ($x:expr, $($xs:tt)+) => {
      max($x,max!($($xs)+))
    };
  }

#[allow(unused_macros)]
macro_rules! min {
    ($x:expr) => {
      $x
    };
    ($x:expr, $($xs:tt)+) => {
      min($x,min!($($xs)+))
    };
  }

#[allow(unused_macros)]
macro_rules! debug {
    ($($a:expr),*) => {
        eprintln!(concat!($(stringify!($a), " = {:?}, "),*), $($a),*);
    }
}

fn main() {
    input! {
    n: usize,
    k: usize,
    s: Chars,
    }

    let mut nums = vec![];
    let mut now = 1;
    let mut cnt = 0;

    for i in 0..n {
        if s[i] == (b'0' + now as u8) as char {
            cnt += 1;
        } else {
            nums.push(cnt);
            now = 1 - now;
            cnt = 1;
        }
    }
    if cnt != 0 {nums.push(cnt);}

    if nums.len() % 2 == 0 {nums.push(0);}

    let add = 2 * k + 1;
    let mut  ans = 0;

    let mut left =0;
    let mut right = 0;
    let mut tmp = 0;

    debug!(nums);

    let mut i = 0;
    for _ in 0..nums.len() {

        let nextleft = i;
        let nextright = min!(i + add, nums.len());

        while nextleft > left {
            tmp -= nums[left];
            left +=1;
        }

        while nextright > right {
            tmp += nums[right];
            right+=1;
        }

        ans = max!(tmp, ans);
        i +=2;
        if i >= nums.len() {
            break;
        }
    }
    println!("{}", ans);;
}