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 C++14 (Clang 3.8.0) (judge verdict: Wrong Answer)

#include <algorithm>
#include <cmath>
#include <cstdio>
#include <deque>
#include <iomanip>
#include <iostream>
#include <map>
#include <queue>
#include <set>
#include <stack>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
using std::cerr;
using std::cin;
using std::cout;
using std::endl;

int main(void) {
  cout << std::fixed << std::setprecision(10);
  cin.tie(0);
  std::ios::sync_with_stdio(false);
  int n, k;
  cin >> n >> k;
  std::string s;
  cin >> s;
  std::bitset<100001> bit;
  for (int si = 0; si < s.size(); si++) {
    if (s[si] == '0') {
      bit[si] = false;
    } else {
      bit[si] = true;
    }
  }
  int left = 0, right = 0;
  int chain;
  int result;
  if (bit[left]) {
    chain = 0;
  } else {
    chain = 1;
    while (right < n && !bit[right]) {
      right++;
    }
  }
  result = right - left + 1;
  while (right < n - 1) {
    right++;
    // cerr << "\033[93m" << left << " " << right << "\033[m" << endl;
    if (bit[right]) {
      // nothing
    } else {
      if (chain < k) {
        while (right < n && !bit[right]) {
          right++;
        }
        chain++;
      } else {
        while (left < n && bit[left]) {
          left++;
        }
        while (left < n && !bit[left]) {
          left++;
        }
        while (right < n && !bit[right]) {
          right++;
        }
      }
    }
    result = std::max(result, right - left + 1);
  }
  result = std::max(result, right - left + 1);
  cout << result << endl;

  return 0;
}