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.*;

/**
 * first
 */
public class first {


    public static void main(String[] args) {
        Scanner sr = new Scanner(System.in);
        int n = sr.nextInt();
        int k = sr.nextInt();
        String input = sr.next();
        int sub_index = 0;

        for (int i = n-1; i >= 0 ; i--) {
            if(input.substring(0, i).equals(input.substring(n-i))){
            sub_index = i;
            break;
            }
        }

        System.out.print(input);
        for(int i = 1; i < k; i++) System.out.print(input.substring(sub_index));

        
        sr.close();
    }
}