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: Wrong Answer)

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

#define MOD 998244353

#define MIN(a,b) ((a)<(b)?(a):(b))
#define MAX(a,b) ((a)>(b)?(a):(b))

typedef long long int64;

int main(void){
    int N,K,ans=0;
    scanf("%d %d",&N,&K);

    char s[N];

    char R;

    scanf("%c",&R);
    

    for(int i=0;i<N;i++){
        scanf("%c",&s[i]);
    }

    int rev[N];
    int num=0;
    char state=s[0];
    int j=0;

    for(int i=0;i<N;i++){
        if(s[i]!=state){
            state=s[i];
            rev[j]=num;
            //printf("%d\n",rev[j]);
            num=0;
            j++;
        }
        num++;
    }

    rev[j]=num;
    //printf("%d\n",rev[j]);
    num=0;
    j++;


    int ANS[j];
    int k=0;

    if(s[0]=='1'){
        if(j<=K*2){
            printf("%d",N);
            return 0;
        }else{
            for(int i=0;i+K*2<j;i++){
                ANS[k]=0;
                if(i%2==0){
                    for(int I=0;I<=K*2;I++){
                        ANS[k]+=rev[i+I];
                    }
                }
                k++;
            }
        }
    }else{
        if(j<=K*2){
            printf("%d",N);
            return 0;
        }else{
            for(int i=0;i+K*2<j;i++){
                ANS[k]=0;
                if(i%2){
                    for(int I=0;I<=K*2;I++){
                        ANS[k]+=rev[i+I];
                    }
                }
                k++;
            }
        }
    }

    for(int i=0;i<k;i++){
        ans=MAX(ans,ANS[i]);
    }

    printf("%d",ans);
    
    
    return 0;
}