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
{
	public static void main (String[] args) throws java.lang.Exception
	{
		Scanner sc = new Scanner(System.in);
	
	
		    int n=sc.nextInt();
		    int k = sc.nextInt();
		    String  s = sc.next();
		    int p=n/2;
		    String s3 ="";
		    int p1=n-1;
		    while(p1!=0){
		        String s1 = s.substring(0,p1);
		        String s2 = s.substring(n-p1,n);
		        if(s1.equals(s2)){
		            s3=s.substring(p1,n);
		            break;
		        }
		        else{
		            p1--; continue;
		        }
		        
		    }
		    
		    k--;
		    if(s3.length()==0){
		        String s4 =s;
		    while(k!=0){
		        k--;
		        s+=s4;
		    }
		        
		    }else{
		        while(k!=0){
		        k--;
		        s+=s3;
		    }
		    }
	
		    System.out.println(s);
		
	}
}