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.FileReader;
import java.io.InputStreamReader;
import java.util.Arrays;
import java.util.HashSet;
import java.util.StringTokenizer;
import java.util.TreeSet;

public class Main {

	static final double eps = 1e-9;
	static final long mod = 1000000007; // or 1000000009

	public static void main(String[] args) throws Exception {

		SC scan = new SC();
//		PrintWriter pw = new PrintWriter(System.out);

	int n = scan.nextInt(), k = scan.nextInt()-1, i = 1;
	String t = scan.nextLine(), s = t;
	while(k > 0) {
		if(t.startsWith(s.substring(i))) {
			s += t.substring(s.length() - i);
			k--;
		}
		i++;
	}
	System.out.println(s);
			
//		pw.flush();
	}

	
	
	static void sort(int[] arr) {
		for (int i = 1; i < arr.length; i++) {
			int j = (int) ((i + 1) * Math.random());
			int temp = arr[j];
			arr[j] = arr[i];
			arr[i] = temp;
		}
		Arrays.sort(arr);
	}

	static class SC {
		BufferedReader br;
		StringTokenizer st;

		public SC() throws Exception {
			br = new BufferedReader(new InputStreamReader(System.in));
			st = new StringTokenizer("");
		}

		public SC(String fn) throws Exception {
			br = new BufferedReader(new FileReader(fn));
			st = new StringTokenizer("");
		}

		String nextLine() throws Exception {
			return br.readLine();
		}

		String next() throws Exception {
			while (!st.hasMoreTokens())
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}

		int nextInt() throws Exception {
			return Integer.parseInt(next());

		}

		double nextDouble() throws Exception {
			return Double.parseDouble(next());
		}

		long nextLong() throws Exception {
			return Long.parseLong(next());
		}
	}
}