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: Wrong Answer)

#include <bits/stdc++.h>

using namespace std;


int main()
{
   int N, K;
   string S;

    int count0, count1;
    bool flag0, flag1;
    bool b0, b1;
    vector<int>vec;
    int sum = 0, max = INT_MIN;


    flag0 = flag1 = true;
    b0 = b1 = false;

    count0 = count1 = 0;

   cin >> N >> K;
   cin >> S;
    if (S[0] != '1') {
      vec.push_back(0);
    }

    //create vec
    for (int i = 0; i < N; i++) {
        if (S[i] == '1') {
            if (flag1 == true) {
                count1++;
            }
             flag0 = false;
            if (flag0)
                vec.push_back(count0);
           
            count0 = 0;
            if (i == N-1)
                vec.push_back(count1);
        } else if (S[i] == '0') {
            if (flag0 == true) {
                count0++;
            }
            flag1 = false;
            if (flag1)
                vec.push_back(count1);
            
            count1 = 0;
           if (i == N-1)
                vec.push_back(count0);
        }
    }
    
  

   if ((int)vec.size() % 2 == 0) {
       vec.push_back(0);
   }
   if (((int)vec.size()-2)/2 < K) {
       cout << N << endl;
       return 0;
   }
    for (int i = 0; i+(2*K+1) < (int)vec.size(); i += 2) {
        sum = 0;
        for (int j = i; j < 2*K+1; j++) {
            sum += vec[j];
        }
        if (sum > max) {
            max = sum;
        }
       }
   

   cout << max << endl;
    return 0;   
}