For a given integer K and a string S of length N, we denote power of S, as the length of a longest substring occurring in S at least K times.

Given K and S, find the power of S.

Constraints:

1 <= N <= 10⁶
1 <= K <= N
S consists of latin lowercase letters only

Input format:

In the first line there are two integers K and N separated by a single space. The second line constains string S itself.

Output format:

In one line, output the power of string S for a given K.