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_macros)]
macro_rules ! for_ { ( $ init : stmt ; $ cond : expr ; $ incr : expr , $ body : block ) => ( { $ init ; while $ cond { $ body $ incr ; } } ) ; }

fn main() {
    use std::io::Read;
    let mut buf = String::new();
    std::io::stdin().read_to_string(&mut buf).unwrap();
    let mut iter = buf.split_whitespace();
    
    let _: usize = iter.next().unwrap().parse::<usize>().unwrap();
    let k: usize = iter.next().unwrap().parse::<usize>().unwrap();
    let s: String = iter.next().unwrap().parse::<String>().unwrap();
    
    let mut sum = vec![];
    let mut current = true;
    let mut acc = 0;
    for c in s.chars() {
        match (c, current) {
            ('0', false) | ('1', true) => acc += 1,
            ('0', true) | ('1', false) => {
                sum.push(acc);
                acc = 1;
                current = !current;
            },
            _ => ()
        }
    }
    sum.push(acc);
    if !current {sum.push(0);}

    let mut sum_of_sum: Vec<u64> = vec![0u64;sum.len()+1];
    for i in 0..sum.len() {
        sum_of_sum[i+1] = sum_of_sum[i] + sum[i];
    }

    let mut max = 0u64;
    for_!(let mut i = 0; i <= sum.len(); i+=2, {
        let j = std::cmp::min(sum.len(), i+k*2+1);
        max = std::cmp::max(max, sum_of_sum[j] - sum_of_sum[i]);
    });
    println!("{}", max);
}