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: Accepted)

<?php
/**
 * ABC124
 * D - Handstand
 */

fscanf(STDIN, "%d %d", $n, $k);
$s = trim(fgets(STDIN));

$number_list = [];
$length = strlen($s);

if ($s[0] === '0') {
    $number_list[] = 0;
}
$j = 0;
for ($i = 0; $i < $length;) {
    while ($j < $length and $s[$i] === $s[$j]) {
        $j++;
    }
    $number_list[] = $j - $i;
    $i = $j;
}
if ($s[$length - 1] === '0') {
    $number_list[] = 0;
}

// 累積和
$cumulative_sum_list = [0];
foreach ($number_list as $key => $number) {
    $cumulative_sum_list[$key + 1] = $cumulative_sum_list[$key] + $number;
}

$cumulative_sum_list_length = count($cumulative_sum_list);

$result = 0;

for ($left = 0; $left < $cumulative_sum_list_length; $left += 2) {
    $right = min($left + $k * 2 + 1, $cumulative_sum_list_length - 1);
    $total = $cumulative_sum_list[$right] - $cumulative_sum_list[$left];
    if ($result < $total) {
        $result = $total;
    }
}
 
echo $result, PHP_EOL;