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.util.*;
import java.io.*;

public class Main {
	static final int M = 1000000007;
		static FastReader in = new FastReader();
		static PrintWriter out = new PrintWriter(System.out);
//		static Scanner in = new Scanner(System.in);
//        File file = new File("input.txt");
//        Scanner in = new Scanner(file);
//        PrintWriter out = new PrintWriter(new FileWriter("output.txt"));
    public static void main(String[] args) {
    	
    	
//    	int t = in.nextInt();
//    	while(t-- > 0){
    	int n = in.nextInt(), k = in.nextInt();
    	String t = in.next();
    	int len = getPeriod(t, n);
    	StringBuilder sb = new StringBuilder();
    	k--;
    	while(k-->0) {
    		sb.append(t, 0, len);
    	}
    	sb.append(t);
    	out.print(sb);
    		
//    	}
    	out.close(); 
    }     
   
    static int getPeriod(String t, int n) {
        int[] arr = new int[n];
        for (int i = 1; i < n; ++i) {
            int j = arr[i - 1];
            while (j > 0 && t.charAt(j) != t.charAt(i))
                j = arr[j - 1];
            if (t.charAt(i) == t.charAt(j))
                ++j;
            arr[i] = j;
        }
        return n - arr[n - 1];
    }


	static int gcd(int a, int b) {
    	if(b==0) return a;
    	return gcd(b, a%b);
    }
    
	static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        public FastReader() {
            br = new BufferedReader(new
                    InputStreamReader(System.in));
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

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

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

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

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }
}