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.*;
import java.io.*;

public class p1029A {

	public static void main(String[] args) {
		int n, k;
		String s, t;
		Scanner input = new Scanner(System.in);
		
		String l1 = input.nextLine();
		String[] l1L = l1.split(" ");
		n = Integer.parseInt(l1L[0]);
		k = Integer.parseInt(l1L[1]);
		String l2 = input.nextLine();

		String[] l2L = l2.split(" ");
		t = l2L[0];
		input.close();
		s = new String(t);
	    int p = 1;
	    
		for (int i = 1; i<k; i++) {
			boolean isPrefix = false;
			
			for (int j=p;j<s.length();j++) {
				//check if s[1..len] is a substring of t
				if (t.startsWith(s.substring(j, s.length()))) {
					s = s.concat(t.substring(s.length() - j,t.length()));
					p++;
					isPrefix = true;
					break;
				}
				p++;
			}
			if (!isPrefix) {
				p = s.length()+1;
				s = s.concat(t);
			}
		}
		System.out.println(s);
		
	}
	
}