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.InputStreamReader;
import java.util.Scanner;

public class A {
	public static void main(String[] args) throws Exception {
		// while (true)
		solve();
	}

	// **SOLUTION**
	public static void solve() throws Exception {
		String[] ip = br.readLine().split(" ");
		int n = new Integer(ip[0]);
		int k = new Integer(ip[1]);
		String s = br.readLine();
		String r = s;
		StringBuilder sb = new StringBuilder();
		sb.append(s);
		k -= 1;
		int idx = -1;
		for (int i = s.length() - 1; i > 0; i--) {
			if (idx(i, s, r)) {
				idx = i;
			}
		}

		for (int x = 0; x < k; x++) {
			if (idx != -1) {
				for (int i = s.length() - idx; i < s.length(); i++)
					sb.append(s.charAt(i));
			} else {
				sb.append(s);
			}
		}
		System.out.println(sb.toString());
	}

	private static boolean idx(int x, String s, String r) {
		int j = 0, i = x;
		for (; i < s.length() && j < r.length(); i++, j++) {
			if (s.charAt(i) != r.charAt(j)) {
				return false;
			}
		}
		return true;
	}

	public static InputStreamReader r = new InputStreamReader(System.in);

	public static BufferedReader br = new BufferedReader(r);

	public static Scanner sc = new Scanner(System.in);
}