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.PrintWriter;
import java.util.HashSet;
import java.util.Scanner;

public class ManyEqualSubstrings {

	void solve(Scanner in, PrintWriter out) {
		int l = in.nextInt();
		int k = in.nextInt();
		String t = in.next();

		String[] suff = new String[l - 1];
		HashSet<String> hs = new HashSet();
		for (int i = 1, j = 0; i < l; i++, j++) {
			hs.add(t.substring(0, i));
		}
		int max = Integer.MIN_VALUE;
		for (int i = l - 1, j = 0; i > 0; i--, j++) {
			suff[j] = t.substring(i, l);
			if (hs.contains(suff[j])) {
				max = Math.max(max, suff[j].length());
			}

		}
		String rep = t;
		if (max != Integer.MIN_VALUE) {
			rep = t.substring(max);
		}
		StringBuilder res = new StringBuilder(t);
		while (k > 1) {
			res.append(rep);
			k--;

		}
		out.println(res);

	}

	void run() {
		try (Scanner in = new Scanner(System.in); PrintWriter out = new PrintWriter(System.out);) {
			solve(in, out);
		}
	}

	public static void main(String args[]) {
		new ManyEqualSubstrings().run();
	}
}