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 Perl (v5.18.2) (judge verdict: Wrong Answer)

use strict;
use warnings;
use utf8;

my ($N, $K) = split /\s/, <STDIN>;
my ($S) = split /\s/, <STDIN>;
my (@S) = split //, $S;
use Data::Dumper;
#print Dumper \@S;

# 0 が始まる位置を index として、何個連なるかを要素で持つ
my @array;

my $current = $S[0];
my $mode = $current eq 1 ? 1 : 0;

my @ans;
my $cnt = 0;

for (my $i = 0; $i < @S; $i++) {
    if ($S[$i] eq $current) {
        $cnt++;
    } else {
        if ($S[$i] eq 0) {
            push @array, $cnt;
        } else {
            push @array, -$cnt;
        }
        $current = $S[$i];
        $cnt = 1;
    }
}
if ($cnt > 0) {
    if ($current eq 0) {
        push @array, -$cnt;
    } else {
        push @array, $cnt;
    }
}


my $kk = $K * 2 + ($current eq 1 ? 1 : 0);
my $kkk = $kk;
my $ans = 0;
my $max = 0;
my $cur = 0;

my $dust = $current eq 1 ? $array[0] - $array[1] : -$array[0];
for (my $i = 0; $i < $kk; $i++) {
    if ($i < @array) {
        $cur += 0 < $array[$i] ? $array[$i] : -$array[$i];
    }
}

#print Dumper \@array;
#printf "%s\n", $cur;
$max = $cur;

for (my $i = $kk; $i < @array; $i += 2) {
    $cur -= $array[$i];
    if ($i + 1 < @array) {
        $cur += $array[$i+1];
    }
    $cur -= $dust;
    #printf "%s\n", $cur;
    if ($max < $cur) {
        $max = $cur;
    }

    #printf "@ %s\n", join " ", $i, $i - $kk + 2, $kk, scalar(@array);
    $dust = $array[$i - $kk + 2];
    $dust -= defined $array[$i - $kk + 1 + 2] ? $array[$i - $kk + 1 + 2] : 0;
}

printf "%s\n", $max;