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 proconio::input;

fn main() {
  input! {
    _n: usize,
    k: usize,
    s: String,
  }
  let s = s.chars().collect::<Vec<char>>();
  let k = 2 * k + 1;
  let mut stack: Vec<usize> = vec![];
  
  if s[0] == '0' {
    stack.push(0);
  }
  
  let mut count = 0;
  let mut last = s[0];
  for c in s {
    if c == last {
      count += 1;
    } else {
      last = c;
      stack.push(count);
      count = 1;
    }
  }

  if count > 0 {
    stack.push(count);
  }

  let mut max = 0;
  let mut total = 0;
  let mut index = 0;
  let mut left = 0;
  let mut right = 0;
  while index < stack.len() {
    let next_left = index;
    let next_right = std::cmp::min(index + k, stack.len());

    while right < next_right {
      total += stack[right];
      right += 1;
    }
    
    while left < next_left {
      total -= stack[left];
      left += 1;
    }

    max = std::cmp::max(max, total);
    index += 2;
  }

  println!("{}", max);
}