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::min;
use std::io::stdin;
use std::io::Error;
use std::io::Read;

#[derive(Debug)]
struct Input {
    n: u32,
    k: u32,
    s: Vec<ContinuousCharacters>,
}

#[derive(Debug)]
struct ContinuousCharacters {
    c: char,
    n: u32,
}

fn handle_input(input_str: String) -> Result<Input, Error> {
    let mut iter = input_str.split_whitespace();
    let n: u32 = iter.next().unwrap().parse().unwrap();
    let k: u32 = iter.next().unwrap().parse().unwrap();
    let s = iter.next().unwrap();
    let mut vec = Vec::new();
    vec.push(ContinuousCharacters { c: ' ', n: 0 });
    for c in s.chars() {
        if let Some(tail) = vec.last_mut() {
            if tail.c == c {
                tail.n += 1;
                continue;
            }
        }
        vec.push(ContinuousCharacters { c: c, n: 1 });
    }
    Ok(Input { n: n, k: k, s: vec })
}

fn handle_output(input: Input) -> Result<String, Error> {
    let mut max_continuation = 0;
    for i in 1..input.s.len() {
        let node = input.s.get(i).unwrap();
        if node.c == '0' {
            let sum = input
                .s
                .get(i - 1..min(i + 2 * input.k as usize, input.s.len()))
                .unwrap_or_default()
                .iter()
                .fold(0, |acc, x| acc + x.n);
            if sum > max_continuation {
                max_continuation = sum;
            }
        } else {
            if node.n > max_continuation {
                max_continuation = node.n;
            }
        }
    }
    Ok(format!("{}", max_continuation))
}

fn main() {
    let mut input_str = String::new();
    let stdin = stdin();
    stdin.lock().read_to_string(&mut input_str).unwrap();
    let input = handle_input(input_str).unwrap();
    let output = handle_output(input).unwrap();
    println!("{}", output);
}