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++ (Clang 3.8.0) (judge verdict: Runtime Error)

#include <iostream>
using namespace std;

char input[10010];

int main()
{
    input[0] = '1';
    int n,k;
    cin >> n >> k;
    cin >> &input[1];

    char *start,*cur;
    start = cur = input;
    int max = 0;

    while(*cur)
    {
        while(*cur && *cur == '1') cur++;
        if(!k) break;
        while(*cur && *cur == '0') cur++;
        k--;
    }
    max = cur - start - 1;
    while(*cur)
    {
        while(*start == '1') start++;
        while(*start == '0') start++;
        while(*cur && *cur == '0') cur++;
        while(*cur && *cur == '1') cur++;
        if (max < cur - start) max = cur - start;
    }

    cout << max << endl;
}