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: Accepted)

my ($n, $k) = split(/\s+/, <STDIN>);
my ($s) = split(/\s+/, <STDIN>);

my (@zero, @one) = ();
push @zero, 0 for (1..$k);
push @one,  0 for (0..$k);
my $len = 0;
my $max = 0;

my $last = -1;
my $cont = 0;
for my $i (split(//, $s)) {
    #print "i=$i, ";
    if ($i == $last) {
	$cont++;
    } else {
	if ($last == 1) {
	    my $j = shift @one;
	    push @one, $cont;
	    $len += $cont - $j;
	    $max = $len if $max < $len;
	} elsif ($last == 0) {
	    my $j = shift @zero;
	    push @zero, $cont;
	    $len += $cont - $j;
	}
	$last = $i;
	$cont = 1;
    }
    #print "max=$max, one=",join(" ", @one), ", zero=", join(" ", @zero), "\n";
}
if ($last == 1) {
    my $j = shift @one;
    push @one, $cont;
    $len += $cont - $j;
    $max = $len if $max < $len;
} elsif ($last == 0) {
    my $j = shift @zero;
    push @zero, $cont;
    $len += $cont - $j - shift @one;
    $max = $len if $max < $len;
}

print "$max\n";