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.*;
import java.io.*;
import java.util.regex.*;
public class Main {
    public static void main(String[] args) {
        Scanner s=new Scanner(System.in);
        int n=s.nextInt();
        int k=s.nextInt();
        s.nextLine();
        String a=s.nextLine();
        int[] pre=new int[n+1];
        pre[0]=-1;
        int now=-1;
        for(int i=1;i<=n;i++){
            while(now>=0&&a.charAt(i-1)!=a.charAt(now))
                now=pre[now];
            now++;
            pre[i]=now;
        }
        System.out.print(a);
        for(int i=1;i<k;i++)
            System.out.print(a.substring(pre[n]));
    }
}