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 <stdlib.h>//random,NULL
#include <string.h>
#include <time.h>
#include <unistd.h>//sleep()
#include <math.h>
#include <stdbool.h>

#define rep(i,n) for(int i=0; i<((int)n); i++)
#define REP(i,n) for(int i=0; i<=((int)n); i++)
#define srep(i,a,n) for(int i=a; i<((int)n); i++)
#define SREP(i,a,n) for(int i=a; i<=((int)n); i++)
#define rrep(i,n) for(int i=n-1; i>=0; i--)
#define RREP(i,n) for(int i=n; i>=0; i--)
#define INF 1000000000

int max(int a, int b){
  if(a>=b){
    return a;
  }
  else{
    return b;
  }
}

int main(){
  char buf[1024];
  char buf2[100010];
  int N,K;

  fgets(buf,sizeof(buf),stdin);
  sscanf(buf, "%d %d", &N, &K);

  fgets(buf2,sizeof(buf),stdin);

  int *count=(int *)malloc(sizeof(int)*N);
  int index=0;
  int temp=1;

  srep(i,1,N){
    if(buf2[i]!=buf2[i-1]){
      count[index]=temp;
      temp=1;
      index++;
      if(i==N-1){
        count[index]=temp;
      }
    }
    else{
      temp++;
      if(i==N-1){
        count[index]=temp;
      }
    }
  }
  //count[index]まで埋まっている。

  int k=2*K+1;

  int ans;
  if(k-1>=index){
    ans=N;
  }
  else{
    int max_ans=0;
    int start=0;
    int end=index;
    if(buf2[0]=='0'){
      rep(i,k-1){
        max_ans+=count[i];
      }
      start=1;
    }
    if(buf2[N-1]=='0'){
      temp=0;
      srep(i,index-k+2,index+1){
        temp+=count[i];
      }
      end=end-1;
      max_ans=max(temp, max_ans);
    }

    temp=0;
    if(start+k<end+1){
      srep(i,start,start+k){
        temp+=count[i];
      }
      max_ans=max(max_ans,temp);
      int ele=start+2;
      while(ele<end-k+2){
        temp=temp-count[ele-2]-count[ele-1]+count[ele+k-2]+count[ele+k-1];
        max_ans=max(max_ans, temp);
        ele+=2;
      }
    }
    
    ans=max_ans;
  }

  printf("%d\n", ans);

  return 0;


}