Problem: 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 ... r].

Your task is to construct such string s of minimum possible length that there are exactly k positions i such that s[i ... 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 ≤ n, k ≤ 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.

Examples

Input

3 4
aba


Output

ababababa


Input

3 2
cat


Output

catcat

Solution (in JAVA):

Solution:
import java.util.Scanner;

public class ManyEqSubStr {
	public static void main(String[] args) {

		Scanner in = new Scanner(System.in);
		int n = in.nextInt(), k = in.nextInt(), i, r = 0;
		String s = in.next();
		in.close();

		for (i = 0; i < n; i++) {
			if (s.substring(0, i).equals(s.substring(n - i)))
				r = i;
		}
		System.out.print(s);
		for (i = 0; i < k - 1; i++) {
			System.out.print(s.substring(r));
		}
	}
}