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 Sol
{
    public static void main (String[] args) throws java.lang.Exception
    {
        int a,i,j,temp=0;
        String x,y;
        Scanner sc=new Scanner(System.in);
        //System.out.println(" ");
        int t=sc.nextInt();
        a=sc.nextInt();
        String s=sc.next();
        for(i=0;i<t-1;i++)
        {
        	x=s.substring(0,i+1);
        	y=s.substring(t-i-1);
        	if(x.equals(y))
        	{
        		if(temp<(i+1))
        		temp=(i+1);
        	}
        }
        String fin=s.substring(0,t-temp);
        for(i=1;i<a;i++)
        System.out.print(fin);
        System.out.print(s);
    }
}