Novel

Today, September 24, is a very important day for Seohyeon, a boy who loves literature. It is the day the novel he spent years writing is released to the world!

Seohyeon's novel can be represented as a string $S$ of length $N$. For convenience, $S$ consists only of lowercase English letters. No characters other than lowercase letters, including spaces or newline characters, appear in $S$.

While reviewing the final draft, Seohyeon found a serious problem. If $K$ or more identical characters appear consecutively in one line, the readability drops badly!

To spare readers from discomfort, Seohyeon wants to choose a page width $L$, an integer from 1 to $N$, so that this case does not occur. A narrower page is harder to read, so he wants $L$ to be the largest possible value.

When the width is set to $L$, the first $L$ characters of $S$ are shown on the first line, the next $L$ characters on the next line, and so on, with $L$ characters per line. Only the last line may show fewer than $L$ characters.

SNUPC ends at the same time Seohyeon's novel is published, so he must revise the book quickly. Find the largest valid value of $L$.

The first line contains $N$ and $K$, separated by a space. ($2\le N\le 100\,000$; $2\le K\le N$)

The second line contains the string $S$ of length $N$, made of lowercase English letters.

Print the maximum possible width.