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 in = new Scanner(System.in);
		int n=in.nextInt();
		int k=in.nextInt();
		String t=in.next();
		in.close();
		int s=n;
		for(int i=1;i<n;i++) {
			int j=0;
			while(i+j<n&&t.charAt(j)==t.charAt(i+j)) {
				j++;
			}
			if(i+j==n) {
				s=i;
				break;
			}
		}
		String p = (s==n)? t:t.substring(n-s, n);
		for(int i=1;i<k;i++)
			t+=p;
		System.out.println(t);
		
	}
}