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)

mod reader {
    use std;

    macro_rules! read_line((  ) => {
                           {
                           let mut input = String :: new (  ) ; std :: io ::
                           stdin (  ) . read_line ( & mut input ) . unwrap (
                           ) ; input } } ;);

    pub fn read_to_vec<T: std::str::FromStr>() -> Vec<T> {
        read_line!().split_whitespace().map(|e|
                                                e.parse().ok().unwrap()).collect()
    }

	pub fn read_str() -> String { read_line!().trim().to_owned() }
}
use reader::*;

#[macro_use]
mod misc {
    #[macro_export]
    macro_rules! bind_from_vec((
                               $ ( $ variable : ident ) , + = $ vector : expr
                               ) => {
                               let mut v = $ vector . clone (  ) . into_iter (
                                ) ; $ (
                               let $ variable = v . next (  ) . unwrap (  ) ;
                               ) + } ;);
}

use std::collections::HashMap;

fn main() {
    bind_from_vec!(n , k = read_to_vec :: < usize > (  ));
    let s = read_str();
    let mut uprights: HashMap<i32, i32> = HashMap::new();
    let mut start: i32 = 0;

    uprights.insert(-1, 1);
    for (i, c) in s.chars().enumerate() {
        match c {
            '0' => {
                if start == (i as i32) { uprights.insert(start, 0); }
                *uprights.get_mut(&start).unwrap() += 1;
            }
            '1' => { start = (i as i32) + 1; }
            _ => { }
        }
    }
    uprights.insert(n as i32, 1);

    if uprights.len() - 2 <= k { println!("{}" , n); return; }

    let mut uprights: Vec<_> = uprights.iter().collect();

    uprights.sort_by_key(|tuple| tuple.0);

    println!("{}" , ( 1 .. ( uprights . len (  ) - k ) ) . fold (
             0 , | acc , i | std :: cmp :: max (
             acc , uprights [ i + k ] . 0 - (
             uprights [ i - 1 ] . 0 + uprights [ i - 1 ] . 1 ) ) ));
}