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 PHP7 (7.0.15) (judge verdict: Time Limit Exceeded)

<?php
//error_reporting(0);
list($N,$K) =  explode(" ",trim(fgets(STDIN)));
$S = trim(fgets(STDIN));
//$H=explode(" ",trim(fgets(STDIN)));
$len = strlen($S);
$now = 1;
$cnt = 0;
$Nums = array();
for($i=0;$i<$N;$i++) {
  if ($S[$i]==$now?"1":"0") {
    $cnt++;
  }
  else {
    $Nums[]=$cnt;
    $now = 1 - $now;;
    $cnt=1;
  }
}
if ($cnt != 0) {
  $Nums[]=$cnt;
}
if ((count($Nums)%2)==0){
  $Nums[]=0;
}
$Add = 2 * $K + 1;
$ans = 0;
for($i=0;$i<count($Nums);$i+=2)
{
  $tmp = 0;

  $left = $i;
  $right = min($i + $Add,count($Nums));
  for($j = $left; $j < $right; $j++) {
    $tmp += $Nums[$j];
  }
  $ans = max($tmp,$ans);
}
printf("%d\n",$ans);