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 PHP (5.6.30) (judge verdict: Accepted)

<?php
fscanf(STDIN,"%d %d",$N,$K);
$S=strval(trim(fgets(STDIN)));
$length = strlen($S);
$array1 = [];
$array0 = [];

while(substr($S,0,1) !== false){
  if(substr($S,0,1) === "1"){
    if(strpos($S,"0") === false){
      $array1[] = strlen($S);
      $array0[] = 0;
      break;
    }else{
      $S = substr($S,strpos($S,"0"),strlen($S)-1);
      $array1[] = $length-strlen($S);
      $length = strlen($S);
    }
  }else{
    $array1[] = 0;
  }
  if(substr($S,0,1) === "0"){
    if(strpos($S,"1") === false){
      $array0[] = strlen($S);
      break;
    }else{
      $S = substr($S,strpos($S,"1"),strlen($S)-1);
      $array0[] = $length-strlen($S);
      $length = strlen($S);
    }  
  }else{
    $array0[] = 0;
  }
}

$size = count($array1);
if($K>=$size){
  $max = array_sum($array1)+array_sum($array0);
}else{
  $value = 0;
  $max = $array1[0]+$array0[0];
  for($i=0;$i<$size-$K+1;$i++){
    if($i===$size-$K && $i===0){
      for($j=0;$j<$K;$j++){
        $value += $array1[$i+$j];
      }
    }elseif($i===0){
      for($j=0;$j<$K+1;$j++){
        $value += $array1[$i+$j];
      }
    }elseif($i===$size-$K){
      //何もしない
    }else{
      $value += $array1[($K-1)+$i+1];
    }
    if($i===0){
      for($j=0;$j<$K;$j++){
        $value += $array0[$i+$j];
      }
    }else{
      $value += $array0[($K-1)+$i];
    }
    if($value > $max){
      $max = $value;
    }
    $value -= $array1[$i];
    $value -= $array0[$i];
  }
}
echo $max;