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

list($n, $k) = getLineExploded();
$s = getOneLine();

$iEnd = count(str_split($s)) - 1;

$maxLength = 0;
$tmp = [];
$before = -1;

foreach (str_split($s) as $i => $char) {
    // 初期化
    if (count($tmp) == 0) {
        $tmp[] = [
            'count' => 0,
            'reverseCount' => 0,
        ];
    }

    // var_dump("index:" . $i . ", char:" . $char);
    if ($char == 1) {
        foreach ($tmp as &$_tmp) {
            $_tmp['count'] = $_tmp['count'] + 1;
            if ($before == 0) {
                $_tmp['reverseCount']++;
            }
        }
        if ($before == 0) {
            $tmp[] = [
                'count' => 1,
                'reverseCount' => 0
            ];
        }
        $before = 1;
    } else {
        foreach ($tmp as $tmpI => &$_tmp) {
            if ($k <= $_tmp['reverseCount']) {
                if ($maxLength < $_tmp['count']) {
                    $maxLength = $_tmp['count'];
                }
                unset($tmp[$tmpI]);
                continue;
            }
            $_tmp['count'] = $_tmp['count'] + 1;
        }
        $before = 0;
    }

    // var_dump($tmp);

    if ($i == $iEnd) {
        foreach ($tmp as $tmpI => &$_tmp) {
            if ($maxLength < $_tmp['count']) {
                $maxLength = $_tmp['count'];
            }
        }
    }
}




println($maxLength);






function println($str)
{
    echo $str . "\n";
}

function sprintlnFormat($format, $str)
{
    println(sprintf($format, $str));
}

function getOneLine()
{
    $str = trim(fgets(STDIN));
    return $str;
}

function getLineExploded($delimiter = ' ')
{
    $str = getOneLine();
    $ret = explode($delimiter, $str);
    return $ret;
}