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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;

public class cf1029a {
    public static void main(String[] args) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        String[] inp = br.readLine().split(" ");
        int n = Integer.parseInt(inp[0]);
        int k = Integer.parseInt(inp[1]);

        String s = br.readLine();
        StringBuilder sb = new StringBuilder();
        int[] p = new int[n];
        char[] t = s.toCharArray();

        for (int i = 1; i < t.length; ++i) {
            int j = p[i - 1];
            while (j > 0 && t[j] != t[i])
                j = p[j - 1];
            if (t[i] == t[j])
                ++j;
            p[i] = j;
        }

        int len = t.length - p[n-1];

        for (int i = 0; i < k-1; i++) {
            System.out.print(s.substring(0,len));
        }

        System.out.print(s);
    }
}