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 T506 {
	public static void main(String[] args) {
		Scanner sc=new Scanner(System.in);
		int n=sc.nextInt(),k=sc.nextInt(),same=0;
		String t=sc.next(),news="";
		boolean ok=false;
		for(int i=1;i<n;i++){
			if(t.charAt(0)==t.charAt(i)){
				ok=true;
				for(int j=i;j<n;j++){
					if(t.charAt(j)!=t.charAt(j-i)){ok=false;break;}
				}
				if(ok){
					same=i;
					break;
				}
			}
		}
		if(ok){
			news=t.substring(n-same);
		}else{
			news=t;
		}
		for(int i=1;i<k;i++){
			t+=news;
		}
		System.out.println(t);
	}
}