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)

($n,$k)=glob<>;$_=<>;
$f=substr($_,0,1);
$l=substr($_,-1,1);
chomp;
s/(.)(?!\1)/\1A\2/g;
@s=map{length($_)}split(A,$_);
if ($#s==0){
    print@s;
    exit;
}
$s[$_]+=$s[$_-1] for(1..$#s);
push(@s,$s[$#s]) if $l<1;
$L=$#s;
$d=($k*2+1<=$L)?$k*2+1:$L;
for ($i=1-$f;$i<$L;$i+=2){
    $c=$s[$i];
    $c-=$s[$i-$d] if($i-$d>=0);
    $mx=($mx>$c)?$mx:$c;
}
print$mx