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.BufferedInputStream;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.util.StringTokenizer;

public class Main {

	static InputReader scan = new InputReader(new BufferedInputStream(System.in));
	static int n,k;
	static char[] data;
	public static void main(String[] args) {
		n=scan.nextInt();
		k=scan.nextInt();
		String model=scan.next();
		data=model.toCharArray();
		int len=find();
		StringBuffer sb = new StringBuffer();
		sb.append(data);
		for (int i = 1; i < k; i++) {
			sb.append(model.substring(len));
		}
		System.out.println(sb);
	}
	
	static int find(){
		int ans=n;
		for (int i = 1; i < n; i++) {
			if(check(i)){
				ans=i;
				break;
			}
		}
		return n-ans;
	}
	
	static boolean check(int i){
		for (int j = 0; j+i< data.length; j++) {
			if(data[j]!=data[j+i])
				return false;
		}
		return true;
	}
	static class InputReader {
		public BufferedReader reader;
		public StringTokenizer tokenizer;

		public InputReader(InputStream stream) {
			reader = new BufferedReader(new InputStreamReader(stream), 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());
		}
	}
}