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)

#![allow(unused_imports)]
use std::io::{ self, Write };
use std::str::FromStr;
use std::cmp::{ min, max };
use std::collections::{ BinaryHeap, VecDeque };

#[allow(unused_macros)]
macro_rules! trace {
    ($var:expr) => {
        let _ = writeln!(&mut std::io::stderr(), ">>> {} = {:?}", stringify!($var), $var);
    };
    ($($args:expr),*) => {
        let _ = writeln!(&mut std::io::stderr(), ">>> {} = {:?}", stringify!($($args),*), ($($args),*));
    };
}

#[allow(unused_macros)]
macro_rules! put {
    ($var:expr) => {
        let _ = writeln!(&mut std::io::stdout(), "{}", $var);
    };
    ($var:expr, $($args:expr),*) => {
        let _ = write!(&mut std::io::stdout(), "{} ", $var);
        put!($($args),*);
    };
}

fn main() {
    let mut sc = Scanner::new();
    let n: usize = sc.cin();
    let k: usize = sc.cin();
    let s: Vec<bool> = sc.cin::<String>().chars().map(|c| c == '1').collect();

    let mut g: Vec<usize> = vec![];
    if !s[0] { g.push(0) };
    {
        let mut last = s[0];
        let mut ac = 1;
        for i in 1..n {
            if last == s[i] {
                ac += 1;
            } else {
                g.push(ac);
                last = s[i];
                ac = 1;
            }
        }
        if ac > 0 {
            g.push(ac);
        }
    }

    // trace!(&s);
    // trace!(&g);

    let mut ans = 0;

    let mut x = 0;
    let mut p = 0;
    for i in 0..g.len() {
        if i % 2 == 0 {
            // trace!("add1", g[i]);
            x += g[i];
        } else {
            if p >= k {
                // trace!(g[i], g[i-1-2*k], g[i+0-2*k]);
                x += g[i];
                x -= g[i-1-2*k];
                x -= g[i+0-2*k];
            } else {
                // trace!("add0", g[i]);
                x += g[i];
                p += 1;
            }
        }
        // trace!(x);
        ans = max(ans, x);
    }
    put!(ans);

}

#[allow(dead_code)]
struct Scanner { stdin: io::Stdin, buffer: VecDeque<String>, }
#[allow(dead_code)]
impl Scanner {
    fn new() -> Scanner { Scanner { stdin: io::stdin(), buffer: VecDeque::new() } }
    fn reserve(&mut self) {
        while self.buffer.len() == 0 {
            let mut line = String::new();
            let _ = self.stdin.read_line(&mut line);
            for w in line.split_whitespace() {
                self.buffer.push_back(String::from(w));
            }
        }
    }
    fn cin<T: FromStr>(&mut self) -> T {
        self.reserve();
        match self.buffer.pop_front().unwrap().parse::<T>() {
            Ok(a) => a,
            Err(_) => panic!("parse err")
        }
    }
}