You are given a string $t$ consisting of $n$ lowercase Latin letters and an integer number $k$.

Let's define a substring of some string $s$ with indices from $l$ to $r$ as $s[l \dots r]$.

Your task is to construct such string $s$ of minimum possible length that there are exactly $k$ positions $i$ such that $s[i \dots i + n - 1] = t$. In other words, your task is to construct such string $s$ of minimum possible length that there are exactly $k$ substrings of $s$ equal to $t$.

It is guaranteed that the answer is always unique.

Input

The first line of the input contains two integers $n$ and $k$ ($1 \le n, k \le 50$) — the length of the string $t$ and the number of substrings.

The second line of the input contains the string $t$ consisting of exactly $n$ lowercase Latin letters.

Output

Print such string $s$ of minimum possible length that there are exactly $k$ substrings of $s$ equal to $t$.

It is guaranteed that the answer is always unique.

Samples

3 4
aba

ababababa

3 2
cat

catcat