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 A1029 {

	public static void main(String[] args) {
		int n, k;
		String s;
		Scanner in = new Scanner(System.in);
		n = in.nextInt();
		k = in.nextInt();
		s = in.next();
		int t = n;
		a: for (int i = n - 1; i > 0; i--) {
			if (s.substring(0, i).equals((s.substring(s.length() - i, s.length())))) {
				t = i;
				break a;
			}
		}
		// System.out.println(t);
		StringBuilder res = new StringBuilder();
		if (t == n) {
			for (int i = 0; i < k; i++) {
				res.append(s);
			}
			System.out.println(res.toString());
			return;
		}
		res.append(s);
		for (int i = 0; i < (k - 1); i++) {
			res.append(s.substring(t, s.length()));
		}
		System.out.println(res.toString());
	}

}