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.lang.*;
import java.io.*;
public class Main{
	static Scanner sc = new Scanner(System.in);

	static long getl() {
		return sc.nextLong();
	}
	
	static int geti() {
		return sc.nextInt();
	}
	
	static String gets() {
		return sc.next();
	}
	
	static int[] intArr(int n) {
		int[] arr = new int[n];
		for(int i=0;i<n;i++) arr[i] = geti();
		return arr;
	}
	
	static long[] longArr(int n) {
		long[] arr = new long[n];
		for(int i=0;i<n;i++) arr[i] = getl();
		return arr;
	}
   
	static void print(String s) {
		System.out.print(s);
	}
	
	static void print(long s) {
		System.out.print(s);
	}
	
	static void plarr(long[] arr) {
		for(int i=0;i<arr.length;i++) print(arr[i] + " ");
	}
	
	static void piarr(int[] arr) {
		for(int i=0;i<arr.length;i++) print(arr[i] + " ");
	}
	
	static int preNsuf(String s){
	    int i = 1;
	    int j = s.length()-1;
	    int res1 = 0;
	    int res2 = 0;
	    while(j>=0){
	        String s1 = s.substring(0,i);
	        String s2 = s.substring(j,s.length());
	        if(s1.equals(s2)) {
	            res2 = res1;
	            res1 = s1.length();
	        }
	        i++;j--;
	    }
	    if(res2>s.length())
	    return res1;
	    return res2;
	}
	
    public static void main(String args[]){
      int n = geti();
      int k = geti();
      String s = gets();
      int p = preNsuf(s);
      StringBuilder res = new StringBuilder();
      String ss = new String();
      if(p!=s.length()) ss += (s.substring(0,s.length()-p));
      else ss += (s.substring(0,1));
      
      for(int i=0;i<k;i++) res.append(ss);
      if(p!=s.length()) res.append(s.substring(s.length()-p,s.length()));
      else res.append(s.substring(0,s.length()-1));
      print(res+"\n");
      
    }
}