You are given a string $S$ of length $N$ consisting of `o` and `x`, and integers $M$ and $K$.  
$S$ is guaranteed to contain at least one `x`.

Let $T$ be the string of length $NM$ obtained by concatenating $M$ copies of $S$. Consider replacing exactly $K$ `x`'s in $T$ with `o`.  
Your objective is to have as long a contiguous substring consisting of `o` as possible in the resulting $T$.  
Find the maximum length of a contiguous substring consisting of `o` that you can obtain.

The input is given from Standard Input in the following format:

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

Print the answer as an integer.

-   $N$, $M$, and $K$ are integers.
-   $1 \le N \le 3 \times 10^5$
-   $1 \le M \le 10^9$
-   $1 \le K \le x$, where $x$ is the number of `x`'s in the string $T$.
-   $S$ is a string of length $N$ consisting of `o` and `x`.
-   $S$ has at least one `x`.

9

S= ooxxooooox and T= ooxxooooox.
Replacing x at the third and fourth characters with o makes T= ooooooooox.
Now we have a length-9 contiguous substring consisting of o, which is the longest possible.

8

S= oxxox and T= oxxoxoxxoxoxxox.
Replacing x at the 5,7,8 and 10-th characters with o makes T= oxxooooooooxxox.
Now we have a length-8 contiguous substring consisting of o, which is the longest possible.