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 (GCC 5.4.1) (judge verdict: Runtime Error)

#include <stdio.h>
#include <string.h>
#define maxn 101
#define max(a,b) (a>b?a:b)
static char s[maxn];
static int n,k;
typedef struct{
    int val,len;
} Code;
Code codes[maxn];
static int code_len;
static void solve_code() {
    int pos = 0;
    while(pos<n) {
        int cnt = 1;
        while(s[pos] == s[pos+1]) {
            pos++;
            cnt++;
        }
        codes[code_len].len = cnt;
        codes[code_len].val = s[pos]-'0';
        code_len++;
        pos++;
    }
}
static int solve_ans() {
    int pos = 0, dt = 0;
    int sum = 0;
    int ans = 0;
    int pos0 = 0;
    while(pos < code_len) {
        if(codes[pos].val == 0) {
            if(dt + 1 > k) {
                break;
            }
            dt++;
        }
        sum += codes[pos].len;
        pos++;
    }
    do {
        ans = max(ans,sum);
        if(codes[pos0].val == 0) {
            sum-=codes[pos0].len;
            pos0++;
        }else {
            sum-=codes[pos0].len + codes[pos0+1].len;
            pos0 += 2;
        }
        sum += codes[pos].len;
        sum += codes[pos+1].len;
        pos += 2;
    }while(pos <= code_len);
    return ans;
}
int main() {
    scanf("%d%d",&n,&k);
    scanf("%s",s);
    solve_code();
    printf("%d\n",solve_ans());
}