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F - More Holidays

Score : $500$ points

Problem Statement

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.

Constraints

• $N$, $M$, 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.

Input

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

$N$ $M$ $K$

$S$

Output

Print the answer as an integer.

10 1 2
ooxxooooox

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.

5 3 4
oxxox

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.

30 1000000000 9982443530
oxoxooxoxoxooxoxooxxxoxxxooxox

19964887064