$N$ 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.

Input is given from Standard Input in the following format:

```
$N$ $K$
$S$
```

Print the maximum possible number of consecutive people standing on hands after at most $K$ directions.

-   $N$ 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`.

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.

1

No directions are necessary.