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: Wrong Answer)

#include <stdio.h>
#include <stdlib.h>
#include <string.h>

int
main(void)
{
        int N, K;
        char *S;
        char c;
        int index = 0;
        int num = 0;

        scanf("%d %d\n", &N, &K);
        printf("K = %d\n", K);

        S = malloc((N + 1) * sizeof(char));
        memset(S, 0, (N + 1) * sizeof(char));

        while (scanf("%c", &c) != EOF) {
                if (c == '0') {
                        if (num != 0) {
                                index++;
                                num = 0;
                        }
                } else if (c == '1') {
                        if (num != 1) {
                                index++;
                                num = 1;
                        }
                } else
                        break;

                S[index]++;
                printf("S[%d] = %d\n", index, S[index]);
        }

        int max = 0;
        int x = S[0] == 0 ? 1 : 0;
        if (index > K) {
                for (int i = 0; i < index - K; i++) {
                        int total = 0;
                        for (int j = i; j < i + 2 * K + x; j++)
                                total += S[j];

                        printf("%d - %d = %d\n", i, i + 2 * K + x - 1, total);
                        if (max < total)
                                max = total;
                }
        } else {
                for (int i = 0; i < index + x; i++)
                        max += S[i];
        }

        printf("%d", max);
}