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 Main {
    public static int hd(char[] ch,int a){
        int l= ch.length;
        for(int i=0;i+a<l;i++){
            if(ch[i]!=ch[i+a])
                return 0;
        }
        return a;
    }
    public static void main(String[] args) {
        Scanner scan=new Scanner(System.in);
        int n=scan.nextInt(),k=scan.nextInt();
        String str=scan.next();
        char[] ch=str.toCharArray();
        int box=0;
        block:
        for (int i=1;i<n;i++){
            if(ch[i]==ch[0]){
                {
                    box=hd(ch,i);
                    if(box!=0)
                        break block;
                }

            }
        }
        if(box==0){
            for(int i=0;i<k;i++)
            System.out.print(str);
        }
        else{
            System.out.print(str);
            for(int i=0;i<k-1;i++) {
                for(int j=n-box;j<n;j++)
                    System.out.print(ch[j]);
            }
        }

    }
}