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.*;
public class string {

    public static void main(String[] args) {
        Scanner ler = new Scanner(System.in);
        
        int n =ler.nextInt();
        int m =ler.nextInt(),c=n;
        
        String s=ler.next();
        for (int i = 1; i <n; i++) {
            String a=s.substring(i);
            String b=s.substring(0,n-i);
            if (a.equals(b)) {
                c=i;
                break;
            }
        }
        String R=s.substring(n-c);
        for (int i = 1; i<m; i++) {
            s+=R;
        }
            System.out.println(s);

    }
}