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: Accepted)

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

#define MAX 100000

int char_swich_search(char *a, int len,int index);
// array and length, current_index. output is swiching index.


int main()
{
  int N,K;
  char S[MAX+1];


  scanf("%d %d", &N,&K);
  scanf("%s",S);
  
  int len=strlen(S), flag=S[0]-'0',
    index_array[MAX+1], i=0, r;
  
  index_array[0]=0;
  for(r=1; ;r++)
    {
      i=char_swich_search(S,len,i);
      index_array[r]=i;
      if(i==len)break;
    }
  
  int index_len=r,ini,last,temp,max;
  
  
  if(flag)
    {
      if(index_len/2<=K)
	{
	  printf("%d\n",len);
	  return 0;
	}
      last=2*K+1; ini=0; max=0;
      while(last<=index_len)
	{
	  temp=index_array[last]-index_array[ini];
	  if(max<temp) max=temp;
	  ini+=2; last+=2;
	}
    }
  else
    {
      if((index_len+1)/2<=K)
	{
	  printf("%d\n",len);
	  return 0;
	}
      last=2*K; max=index_array[last];
      ini=1; last+=2;
      while(last<=index_len)
	{
	  temp=index_array[last]-index_array[ini];
	  if(max<temp) max=temp;
	  ini+=2; last+=2;
	}
      
    }
      
  last--;
  temp=index_array[last]-index_array[ini];
  if(max<temp) max=temp;
  
  //  for(i=0;i<=index_len;i++)
  //    printf("i_%d=%d ",i,index_array[i]);
  printf("%d\n",max);
  
  return 0;
}

int char_swich_search(char *a, int len,int index)
{
  int i;
  for(i=index;i<=len;i++)
    {
      if(a[i]!=a[index])break;
    }
  return i;
}