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.Scanner;
public class Main {
	public static void main(String[] args) {
		Scanner scan=new Scanner(System.in);
		int n=scan.nextInt();
		int k=scan.nextInt();
		String s=scan.next();
		int i=0,temp=0;
		int N=s.length();
		String ans=s;
		for(;i<N;i++) {
			if(s.substring(0,i).equals(s.substring(N-i,N))) {
				temp=i;
			}
		}
		
		if( temp==0) {
			for(int j=0;j<k-1;j++) {
			    ans+=s;
			}
		}
		boolean same=true;
		
		
		for(int j=0;j<N;j++) {
		    if(s.charAt(j)!=s.charAt(0)) {
		    	same=false;
		    }
		}
		if(temp>0&&!same) {
			for(int j=0;j<k-1;j++) {
			    ans+=s.substring(temp,N);
			}
		}
		if(temp>0&&same) {
			for(int j=0;j<k-1;j++) {
			    ans+=s.charAt(0);
			}
		}
		System.out.println(ans);
	}	
}