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 void main(String[] args) {
        Scanner reader = new Scanner(System.in);
        StringBuilder stringBuilder = new StringBuilder();
        final int n = reader.nextInt();
        int k = reader.nextInt();
        String s = reader.nextLine();
        s = reader.nextLine();
        stringBuilder.append(new Solver().solve(n,k,s));
        System.out.println(stringBuilder);
    }
}

class Solver{
    public String solve(int n,int k,String s){
        int common = 0;
        for(int i=1;i<n;i++){
            common = i;
            for(int j=0;j<n-i;j++){
                if(s.charAt(i+j) != s.charAt(j)){
                    common = 0;
                    break;
                }
            }
            if(common > 0)
                break;
        }
        StringBuilder stringBuilder = new StringBuilder();
        stringBuilder.append(s);
        for(int i=1;i<k;i++){
            if(common > 0)
                stringBuilder.append(s.substring(n - common));
            else
                stringBuilder.append(s);
        }
        return stringBuilder.toString();
    }



}