Problem: Many countries have such a New Year or Christmas tradition as writing a letter to Santa including a wish list for presents. Vasya is an ordinary programmer boy. Like all ordinary boys, he is going to write the letter to Santa on the New Year Eve (we Russians actually expect Santa for the New Year, not for Christmas). 

Vasya has come up with an algorithm he will follow while writing a letter. First he chooses two strings, s1 anf s2, consisting of uppercase English letters. Then the boy makes string sk, using a recurrent equation sn = sn - 2 + sn - 1, operation '+' means a concatenation (that is, the sequential record) of strings in the given order. Then Vasya writes down string sk on a piece of paper, puts it in the envelope and sends in to Santa. 

Vasya is absolutely sure that Santa will bring him the best present if the resulting string sk has exactly x occurrences of substring AC (the short-cut reminds him оf accepted problems). Besides, Vasya decided that string s1 should have length n, and string s2 should have length m. Vasya hasn't decided anything else.

At the moment Vasya's got urgent New Year business, so he asks you to choose two strings for him, s1 and s2 in the required manner. Help Vasya.

Input

The first line contains four integers k, x, n, m (3 ≤ k ≤ 50; 0 ≤ x ≤ 109; 1 ≤ n, m ≤ 100).

Output

In the first line print string s1, consisting of n uppercase English letters. In the second line print string s2, consisting of m uppercase English letters. If there are multiple valid strings, print any of them.

If the required pair of strings doesn't exist, print "Happy new year!" without the quotes.

Examples

Input

3 2 2 2


Output

AC
AC


Input

3 3 2 2


Output

Happy new year!


Input

3 0 2 2


Output

AA
AA


Input

4 3 2 1


Output

Happy new year!


Input

4 2 2 1


Output

Happy new year!

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;

public class D {

    public void solve() {
        int k = in.nextInt(), x = in.nextInt(), n = in.nextInt(), m = in.nextInt();
        
        int MAX = 100;
        String[][][][] strings = new String[MAX + 1][MAX / 2 + 1][4][4];
        for (int i = 0; i < 4; i++) {
            strings[1][0][i][i] = "" + chars.charAt(i);
        }
        for (int len = 1; len < MAX; len++) {
            for (int occurs = 0; occurs <= MAX / 2; occurs++) {
                for (int first = 0; first < 4; first++ ){
                    for (int second = 0; second < 4; second++) {
                        if (strings[len][occurs][first][second] != null) {
                            for (int third = 0; third < 4; third++) {
                                int newOccurs = occurs + ((second == 0 && third == 2) ? 1 : 0);
                                if (strings[len + 1][newOccurs][first][third] == null) {
                                    strings[len + 1][newOccurs][first][third] = strings[len][occurs][first][second] + (char) ('A' + third);
                                }
                            }
                        }
                    }
                }
            }
        }

        for (int a0 = 0; a0 < 4; a0++) {
            for (int a1 = 0; a1 < 4; a1++) {
                for (int b0 = 0; b0 < 4; b0++) {
                    for (int b1 = 0; b1 < 4; b1++) {
                        int realA1 = a1, realB1 = b1;
                        if (n == 1) {
                            realA1 = a0;
                        }
                        if (m == 1) {
                            realB1 = b0;
                        }
                        for (int count1 = 0; count1 <= 50; count1++) {
                            for (int count2 = 0; count2 <= 50; count2++) {
                                String s1 = strings[n][count1][a0][realA1];
                                String s2 = strings[m][count2][b0][realB1];
                                if (s1 == null || s2 == null) {
                                    continue;
                                }
                                if (get(n, a0, realA1, count1, m, b0, realB1, count2, k) == x) {
                                    out.println(s1);
                                    out.println(s2);
                                    return;
                                }
                            }
                        }
                    }
                }
            }
        }
        out.println("Happy new year!");
    }

    String chars = "ABCD";
    
    private long get(int n, int a0, int a1, long count1, int m, int b0, int b1, long count2, int k) {
        if (k == 2) {
            return count2;
        }
        return get(m, b0, b1, count2, n + m, a0, b1, count1 + count2 + ((a1 == 0 && b0 == 2) ? 1 : 0), k - 1);
    }

    FastScanner in;
    PrintWriter out;

    public void run() {
        try {
            in = new FastScanner();
            out = new PrintWriter(System.out);
            solve();
            out.close();
        } catch (Exception e) {
            e.printStackTrace();
            System.exit(1);
        }
    }

    class FastScanner {
        BufferedReader br;
        StringTokenizer st;

        public FastScanner() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        public FastScanner(String name) {
            try {
                br = new BufferedReader(new FileReader(name));
            } catch (FileNotFoundException e) {
                e.printStackTrace();
            }
        }

        public String nextToken() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(nextToken());
        }

        public long nextLong() {
            return Long.parseLong(nextToken());
        }

        public double nextDouble() {
            return Double.parseDouble(nextToken());
        }
    }

    public static void main(String[] args) {
        new D().run();
    }
}