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.ArrayList;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashMap;
import java.util.Map;
import java.util.Scanner;

public class b {

	public static void main(String[] rgs)
	{
		Scanner s=new Scanner(System.in);

		int n=s.nextInt();
		int t=s.nextInt();
		
		String str=s.next();

		String pat="";
		String temp="";
	
		for(int i=0;i<n;i++) {
			temp=temp+str.charAt(i);
			int count=0;
			for(int j=0;j<str.length();j++) {
				if(count==temp.length()) {
					count=0;
				}
				pat=pat+temp.charAt(count);
				count++;
			}
			if(pat.equals(str)) {
				break;
			}else {
				pat="";
			}
		}
		//System.out.println(temp);
		String ans="";
	for(int i=0;i<t-1;i++) {
		ans=ans+temp;
	}
	
	ans=ans+str;
	System.out.println(ans);
		
	}
}