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.lang.*;
import java.math.*;

public class D {
	public void run() throws Exception {
		FastScanner sc = new FastScanner();
		
		int n = sc.nextInt();
		int k = sc.nextInt();
		String t = sc.next();
		boolean ok = false;
		int ind = -1;
		String ans = "";
		outer:
		for (int i = 1; i<n; i++) {
			if (t.charAt(0) == t.charAt(i)) {
				for (int j = i; j<n; j++) {
					if (t.charAt(j-i) != t.charAt(j)) continue outer;
				}
				ok = true;
				ind = i;
				break;
			}
		}
	//	System.out.println(ok + " " + ind);
		if (ok) {
			ans+=t;
			for (int i = 0; i<k-1; i++) {
				ans+=t.substring(t.length()-ind,t.length());
			}
		}
		else {
			for (int i = 0;i<k; i++) {
				ans+=t;
			}
		}
		System.out.println(ans);
	}
	static class FastScanner {
		public BufferedReader reader;
		public StringTokenizer tokenizer;

		public FastScanner() {
			reader = new BufferedReader(new InputStreamReader(System.in), 32768);
			tokenizer = null;
		}

		public String next() {
			while (tokenizer == null || !tokenizer.hasMoreTokens()) {
				try {
					tokenizer = new StringTokenizer(reader.readLine());
				} catch (IOException e) {
					throw new RuntimeException(e);
				}
			}
			return tokenizer.nextToken();
		}

		public int nextInt() {
			return Integer.parseInt(next());
		}

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

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

		public String nextLine() {
			try {
				return reader.readLine();
			} catch (IOException e) {
				throw new RuntimeException(e);
			}
		}

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