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 / /, <>;
my $s = <>;
chomp $s;

my(@l);

my $c = 0;
my $now = 1;

for(my $i = 0; $i < length $s; $i++){
    if(substr($s, $i, 1) == $now){
        $c++;
    } else {
        push @l, $c;
        $now = 1 - $now;
        $c = 1;
    }
}

push @l, $c;

my $max = 0;

for(my $i = 0; $i < $k * 2 + 1; $i++){
    $max += $l[$i];
}

my $nowx = $max;

for(my $ex = 0, $in = $k * 2 + 1; $in <= $#l; $ex+=2, $in+=2){
    my $newnow = $nowx - $l[$ex] - $l[$ex+1] + $l[$in] + $l[$in+1];
    if($newnow > $max){$max = $newnow;}
    $nowx = $newnow;
}

print $max;