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 Main {
	public static void main(String[] args) {
		Scanner scan = new Scanner(System.in);
		int n = scan.nextInt();
		int k = scan.nextInt();
		String t = scan.next();
		int a = 1;
		while (a<n) {
			int b = 0;
			while (a+b<n&&t.charAt(b)==t.charAt(a+b)) {
				b++;
			}
			if (a+b==n) 
				break;
			a++;
		}
		int x = 1;
		System.out.print(t);
		while (x<k) {
			int y = n-a;
			while (y<n) {
				System.out.print(t.charAt(y));
				y++;
			}
			x++;
		}
	}

}