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: Wrong Answer)

<?php

fscanf(STDIN, '%d %d', $N, $K);
fscanf(STDIN, '%s', $S);

$count = 1;
$index = 0;
$counts = array_fill(0, $N, 0);

for ($i=1; $i < $N ; $i++) { 
    if ( $S[$i] !== $S[$i-1] ) {
        $counts[$index] = $count;
        $index++;
        $count = 1;
    } else {
        $count++;
    }
}
$counts[$index] = $count;
$lastIndex = $index;

$i = 0;
if ( $S[0] == 0 ) {
    $start = max(0, 2 * $i - 1);
    $end = 2 * $i - 1 + 2 * $K;
} else {
    $start = 2 * $i;
    $end = 2 * $i + 2 * $K;
}
$tempMax = array_sum(array_slice($counts, $start, $end-$start+1));
$temp = $tempMax;


for ($i=0; $i <$lastIndex+1 ; $i++) {
    if ( $i == 0 && $S[0] == 0 ) {
        $temp = $temp - $counts[$start + 2 * $i];
    } else {
        $temp = $temp - $counts[$start + 2 * $i] - $counts[$start + 2 * $i + 1];
    }
    $temp = $temp + $counts[$end + 2 * $i + 1] + $counts[$end + 2 * $i + 2];

    if ($tempMax < $temp) {
        $tempMax = $temp;
    }

    if ( $end + 2 * $i + 2 >= $lastIndex ) {
        break;
    }
}

echo (int) $tempMax;

?>