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 javax.swing.plaf.synth.SynthOptionPaneUI;
import java.util.Scanner;
import java.util.*;
import java.util.logging.XMLFormatter;

import static java.lang.Math.*;


public class Main {
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int n = in.nextInt();
        int k = in.nextInt();
        String s = in.next();
        int len = 0;
        for (int i = 1; i < n; i++) {
            if (s.substring(0, i).equals(s.substring(s.length() - i, s.length()))) {
                len = i;
            }
        }
        String t = s.substring(len, s.length());
        String res = s;
        for (int i = 0; i < k - 1; i++) {
            res += t;
        }
        System.out.println(res);
    }
}