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 ManyEqualSubstrings2 {

	public static void main(String[] args) {
		Scanner input= new Scanner(System.in);
		
		int n = input.nextInt(), k = input.nextInt();
		input.nextLine();
		String t= input.nextLine(), s="";
		input.close();
		int i=0, j=1, sStart=0, b=0, a[]=new int[n];
		
		while(j!=n) if(t.charAt(i)==t.charAt(j++)) a[b++]=j-1;
		b=0;
		
		while(a[b]>0) {
				i=0; j=a[b++]; sStart=0;
				while(j!=n && t.charAt(i)==t.charAt(j)) {sStart++;i++;j++;};
				if(j==n) {
					System.out.print(t);
					while(sStart!=n) s+=t.charAt(sStart++);
					while(--k>0)System.out.print(s);
					System.exit(0);
				}
		}
		while(k-->0)System.out.print(t);
	}
}