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.*;

import static java.lang.Math.*;

public class CF1029A_ManyEqualSubstrings extends PrintWriter {
    public void solve() throws IOException {
        int n = readInt();
        int k = readInt();

        String str = read();

        String repeatedStr = str;

        for (int i = 0; i < n - 1; i++) {
            if (str.substring(0, i + 1).equals(str.substring(n - i - 1))) {
                repeatedStr = str.substring(i + 1);
            }
        }

        StringBuilder result = new StringBuilder(str);
        while (--k > 0) {
            result.append(repeatedStr);
        }

        println(result.toString());
    }

    BufferedReader in;
    StringTokenizer stok;

    public void run() {
        try {
            solve();
            close();
        } catch (Exception e) {
            e.printStackTrace();
            System.exit(abs(-1));
        }
    }

    CF1029A_ManyEqualSubstrings() {
        super(System.out);
        in = new BufferedReader(new InputStreamReader(System.in));
    }

    public static void main(String[] args) {
        try {
            Locale.setDefault(Locale.US);
        } catch (Exception ignored) {
        }
        new CF1029A_ManyEqualSubstrings().run();
    }

    String read() throws IOException {
        while (stok == null || !stok.hasMoreTokens()) {
            String s = in.readLine();
            if (s == null) {
                return null;
            }
            stok = new StringTokenizer(s);
        }
        return stok.nextToken();
    }

    int readInt() throws IOException {
        return Integer.parseInt(read());
    }

    long readLong() throws IOException {
        return Long.parseLong(read());
    }

    double readDouble() throws IOException {
        return Double.parseDouble(read());
    }

    int[] readIntArray(int len) throws IOException {
        int[] a = new int[len];
        for (int i = 0; i < len; i++) {
            a[i] = readInt();
        }
        return a;
    }

    <T> List<T>[] createAdjacencyList(int countVertex) {
        List<T>[] res = new List[countVertex];
        for (int i = 0; i < countVertex; i++) {
            res[i] = new ArrayList<T>();
        }
        return res;
    }
}