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.*;
import java.util.*;
import java.text.*;
import java.math.*;
import java.util.regex.*;

public class ManyEqualSubString{

    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int l=0;
        int n = in.nextInt();
        int k=in.nextInt();
        String t=in.next();
        //System.out.println("*****"+t+"*******");
        for (int p = 1; p < n; ++p) {
		boolean f = true;
		for (int i = 0; i < p; ++i) {
			if (t.charAt(i) != t.charAt(n - p + i)) {
				f = false;
			}
		}
		if (f) {
			l = p;
		}
	}
	System.out.print(t);
	for (int i = 0; i < k - 1; ++i) {
		System.out.print(t.substring(l));
	}
        
                      
                in.close();
    }
}