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.io.BufferedReader;
import java.io.IOException;
import java.util.Scanner;

public class Main{
		
	
	public static void main(String[] args) throws NumberFormatException, IOException{

		Scanner scanner = new Scanner(System.in);
		
		int n = scanner.nextInt();
		int k = scanner.nextInt();
		String t = scanner.next();
		
		String anString = null;
		for(int i = 1; i < t.length(); ++i) {
			String tt = t.substring(i);
			if(tt.equals(t.substring(0, tt.length()))) {
				anString = tt;
				break;
			}
		}
		if (anString == null) {
			anString = t;
		}else {
			int len = anString.length();
		//	System.out.println(len);
			anString = t.substring(len);
		}
		//System.out.println(anString);

		StringBuilder s = new StringBuilder(t);
		while(k-- > 1) {
			s.append(anString);
		}
		
		System.out.println(s);
		
		
		
		
			
		
	}	
}