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;
import java.util.StringTokenizer;

public class Main {
    public static void main(String[] args) {
        int n = ni();
        int k = ni();
        String t = ns();
        char[] st = t.toCharArray();

        int pl = st.length;
        for (int i = 1; i < st.length; i++) {
            boolean ok = true;
            for (int j = 0; j + i < st.length; j++) {
                if (st[j] != st[j + i]) {
                    ok = false;
                    break;
                }
            }
            if (ok) {
                pl = i;
                break;
            }
        }
        String dd;
        if (pl == st.length) {
            dd = t;
        } else {
            dd = t.substring(st.length - pl);
        }

        for (int i = 0; i < k - 1; i++) {
            t += dd;
        }
        System.out.println(t);

    }


    static final int mod = 1000000007;
    static StringBuilder ans = new StringBuilder();
    static Reader in = new Reader();
    static final double eps = 1e-9;

    //////////////////////////////////
    //input functions/////////////////
    static int ni() {
        return Integer.parseInt(in.next());
    }

    static long nl() {
        return Long.parseLong(in.next());
    }

    static String ns() {
        return in.next();
    }

    static double nd() {
        return Double.parseDouble(in.next());
    }

    static int[] nia(int n) {
        int a[] = new int[n];
        for (int i = 0; i < n; i++) a[i] = ni();
        return a;
    }

    static int[] pnia(int n) {
        int a[] = new int[n + 1];
        for (int i = 1; i <= n; i++) a[i] = ni();
        return a;
    }

    static long[] nla(int n) {
        long a[] = new long[n];
        for (int i = 0; i < n; i++) a[i] = nl();
        return a;
    }

    static String[] nsa(int n) {
        String a[] = new String[n];
        for (int i = 0; i < n; i++) a[i] = ns();
        return a;
    }

    static double[] nda(int n) {
        double a[] = new double[n];
        for (int i = 0; i < n; i++) a[i] = nd();
        return a;
    }

    //////output functions////////////////
    static void pr(Object a) {
        ans.append(a + "\n");
    }

    static void pr() {
        ans.append("\n");
    }

    static void p(Object a) {
        ans.append(a);
    }

    static void pra(int[] a) {
        for (int i : a) ans.append(i + " ");
        ans.append("\n");
    }

    static void pra(long[] a) {
        for (long i : a) ans.append(i + " ");
        ans.append("\n");
    }

    static void pra(String[] a) {
        for (String i : a) ans.append(i + " ");
        ans.append("\n");
    }

    static void pra(double[] a) {
        for (double i : a) ans.append(i + " ");
        ans.append("\n");
    }

    static void sop(Object a) {
        System.out.println(a);
    }

    static void flush() {
        System.out.print(ans);
        ans = new StringBuilder();
    }

    static void exit() {
        System.out.print(ans);
        System.exit(0);
    }

    static int min(int... a) {
        int min = a[0];
        for (int i : a) min = Math.min(min, i);
        return min;
    }

    static int max(int... a) {
        int max = a[0];
        for (int i : a) max = Math.max(max, i);
        return max;
    }

    static int gcd(int... a) {
        int gcd = a[0];
        for (int i : a) gcd = gcd(gcd, i);
        return gcd;
    }

    static long min(long... a) {
        long min = a[0];
        for (long i : a) min = Math.min(min, i);
        return min;
    }

    static long max(long... a) {
        long max = a[0];
        for (long i : a) max = Math.max(max, i);
        return max;
    }

    static long gcd(long... a) {
        long gcd = a[0];
        for (long i : a) gcd = gcd(gcd, i);
        return gcd;
    }

    static String pr(String a, long b) {
        String c = "";
        while (b > 0) {
            if (b % 2 == 1) c = c.concat(a);
            a = a.concat(a);
            b >>= 1;
        }
        return c;
    }

    static long powm(long a, long b, long m) {
        long an = 1;
        long c = a;
        while (b > 0) {
            if (b % 2 == 1) an = (an * c) % m;
            c = (c * c) % m;
            b >>= 1;
        }
        return an;
    }

    static int gcd(int a, int b) {
        if (b == 0) return a;
        return gcd(b, a % b);
    }

    static long gcd(long a, long b) {
        if (b == 0) return a;
        return gcd(b, a % b);
    }

    static class Reader {
        BufferedReader reader;
        StringTokenizer tokenizer;

        public Reader() {
            reader = new BufferedReader(new InputStreamReader(System.in), 32768);
            tokenizer = null;
        }

        String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }
    }

}