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.*;
import java.util.*;
public class CF506B {
    static BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
    public static void main(String[]args)throws Exception
    {
        StringTokenizer st = new StringTokenizer(br.readLine());
        String s=br.readLine();
        char cc[]=s.toCharArray();
        int n=Integer.parseInt(st.nextToken());
        int k=Integer.parseInt(st.nextToken());
        int a=0;
        hh: for(int i=1;i<n;i++)
        {
            if(cc[i]==cc[0])
            {
                int aa=0;
                for(int j=i;j<n;j++)
                {
                    if(cc[j]==cc[aa])
                    {
                        aa++;
                        continue;
                    }
                    else
                        continue hh;
                }
                a=aa;
                if(a>0)
                    break;
            }
        }
        String sub=s.substring(a);
        for(int i=1;i<k;i++)
            s=s+sub;
        System.out.println(s);
    }
    public static int[] getarr() throws Exception
    {
        int no=Integer.parseInt(br.readLine());
        int arr[]=new int[no];
        StringTokenizer st=new StringTokenizer(br.readLine());
        for(int i=0;i<no;i++)
            arr[i]=Integer.parseInt(st.nextToken());
        return arr;
    }
}