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 (GCC 5.4.1) (judge verdict: Time Limit Exceeded)

#include <iostream>
// #include <algorithm>
// #include <set>
// #include <map>
using namespace std;

int main()
{
  // 整数の入力
  int N, K;
  cin >> N >> K;
  string S;
  cin >> S;

  int i = 0;
  int max = 0;
  while (i < N)
  {
    char p;
    int count = 0;
    int replaceCount = 0;
    for (int j = i; j < N; j++)
    {
      if (S[j] == '0')
      {
        if (p == '0')
        {
          count++;
        }
        else if (replaceCount < K)
        {
          replaceCount++;
          count++;
        }
        else
        {
          break;
        }
      }
      else
      {
        count++;
      }

      p = S[j];
    }

    if (count > max)
    {
      max = count;
    }

    // 次の探索地点に持っていく
    char pp = S[i++];
    while (pp == S[i] || pp == '1')
    {
      pp = S[i++];
    }
  }
  cout << max << endl;

  return 0;
}