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.io.*;
import java.math.*;
import java.security.*;
import java.text.*;
import java.util.*;
import java.util.concurrent.*;
import java.util.regex.*;

public class Solution {

    private static final Scanner scanner = new Scanner(System.in);
    
    public static void main(String[] args) throws IOException {
        int n = scanner.nextInt();
        int k = scanner.nextInt();
        String s = scanner.next();
        int len = 0;
        for(int i = 1; i < n; i++){
            int possible = 1;
            for(int j = 0; j < n - i; j++){
                if(s.charAt(j) != s.charAt(i + j)){
                    possible = 0;
                    break;
                }
            }
            if(possible == 1)len = Math.max(len, n - i);
            // System.out.println(len + " " + i);
        }
        String s1 = s.substring(0, n - len);
        String s2 = s.substring(n - len);
        for(int i = 0; i < k; i++){
            System.out.print(s1);
        }
        System.out.println(s2);
    }
}