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.HashSet;
import java.util.Scanner;

public class dhuk {

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		int k  =sc.nextInt();
		String str = sc.next();
		int len = 0;
		HashSet<String> set = new HashSet<>();
		
		for(int i=0;i<n;i++){
			set.add(str.substring(0,i+1));
		}
		String res = str;
		for(int i=1;i<n;i++){
			if(set.contains(str.substring(i,n))){
//				System.out.println(str.substring(i,n));
				res = str.substring(n-i,n);
				break;
			}
		}
		System.out.print(str);
		for(int i=0;i<k-1;i++){
			System.out.print(res);
		}
		

	}

}