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 ManyEqualSubstring {
    public static void main(String args[]){
        Scanner sc = new Scanner(System.in);
        int len = sc.nextInt();
        int rep = sc.nextInt();
        String check = sc.next();
        int n = overlap(check);
        System.out.print(check);
        if (n >= 0){
            for (int j = 0; j < rep-1; j++) {
                System.out.print(check.substring(n, check.length()));
            }
        }
    }
    public static int overlap(String str){
        int retval = 0;
        for (int p = 1; p < str.length(); p++){
            if (str.substring(0,p).equals(str.substring(str.length()-p,str.length()))){
                retval = p;
            }
        }
        return retval;
    }
}