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
fscanf(STDIN, '%d %d', $len, $k);
fscanf(STDIN, '%s', $line);
$org = str_split($line);
$map = [];
$now = 1;
$cnt = 0;
for ($i=0; $i < $len; $i++) { 
    if ($org[$i] == $now) {
        $cnt++;
    } else {
        $map[] = $cnt;
        $now = 1 - $now;
        $cnt = 1;
    }
}

if ($cnt) {
    $map[] = $cnt;
}

if (count($map) % 2 == 0) {
    $map[] = 0;
}

$mapLen = count($map);
$tmpArr = array_fill(0, $mapLen + 1, 0);
for ($i=0; $i < $mapLen; $i++) { 
    $tmpArr[$i + 1] = $tmpArr[$i] + $map[$i];
}

$max = 0;
for($i = 0; $i < $mapLen; $i+=2){
    $left = $i;
    $right = min($i + 2 * $k + 1, $mapLen);
    $tmp = $tmpArr[$right] - $tmpArr[$left];

    $max = max($max, $tmp);
}
echo $max;