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 List::Util qw(max sum);
my ($n, $k) = split(/\s+/, <>);
my ($s) = split(/\s+/, <>);

my (@counts) = ();

my $len = length($s);
my $bit = 1;
my $c   = 0;
for (my $i=0; $i<$len; $i++) {
    #print substr($s, $i, 1), "\n";
    if (substr($s, $i, 1) == $bit) {
	$c++;
    } else {
	push @counts, $c;
	$bit = 1-$bit;
	$c = 1;
    }
}
push @counts, $c;
$len = @counts;
push @counts, 0 for (0..$k*2+1);
print "$len, ", join(" ", @counts), "\n";

my $sum = sum(@counts[0..$k*2]);
my $max = $sum;
for (my $out=0,$in=$k*2+1; $out<$len; $in+=2,$out+=2) {
    $sum += $counts[$in]+$counts[$in+1] - $counts[$out]-$counts[$out+1];
    $max = max($max, $sum);
}
print "$max\n";