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.util.*;
import java.math.*;
import java.io.*;

public class D2 {
    public static long time = 0;

    public static void main(String[] args) throws Exception {
        time = System.currentTimeMillis();
        solve();
        out.flush();
    }
    static int TRUE = 1;
    static int FALSE = 0;
    static int k1;
    public static void solve() throws Exception {
        k1 = ni();
        BigInteger target = bi(ni());
        int n1 = ni();
        int m1 = ni();
        for (int i = 0; i <= n1 / 2; i++){
            for (int qq1 = 0; qq1 < 2; qq1++){
                for (int ww1 = 0; ww1 < 2; ww1++){
                    for (int j =0; j <= m1 / 2; j++){
                        for (int qq2 = 0; qq2 < 2; qq2++){
                            for (int ww2 = 0; ww2 < 2; ww2++){
                                if (i * 2 + qq1 + ww1> n1) continue;
                                if (j * 2 + qq2 + ww2> m1) continue;
//                              px(i, j, qq1 == 1, qq2 ==3 2 2 2 1, ww1 == 1, ww2 == 1);
                                BigInteger val = solve(i, j, qq1 == 1, qq2 == 1, ww1 == 1, ww2 == 1);
                                if (val.equals(target)){
                                    String f1 = gen(n1, qq1 == 1, ww1 == 1, i);
                                    String f2 = gen(m1, qq2 == 1, ww2 == 1, j);
                                    pn(f1);
                                    pn(f2);
//                                  px(f1,f2);
                                    return;
                                }
                            }
                        }
                    }
                }
            }
        }
        pn("Happy new year!");
    }
    static String gen(int leng, boolean front, boolean back, int amount){
        char[] fin = new char[leng];
        Arrays.fill(fin, 'Z');
        int start = 0;
        if (front){
            start = 1;
            fin[0] = 'C';
            
        }
        for (int i = 0; i< amount; i++){
            fin[start + i * 2] = 'A';
            fin[start + i * 2 + 1] = 'C';
        }
        if (back){
            fin[leng - 1] = 'A';
        }
        return String.valueOf(fin);
    }
    static class State {
        BigInteger no = BigInteger.valueOf(0);
        boolean front = false;
        boolean end = false;
        static void merge(State s1, State s2, State s3){
            BigInteger fin = s1.no.add(s2.no);
            if (s1.end && s2.front) fin = fin.add(BigInteger.ONE);
            s3.no = fin;
            s3.front = s1.front;
            s3.end = s2.end;
        }
    }
    static State it1 = new State();
    static State it2 = new State();
    static State it3 = new State();
    public static BigInteger solve(int v1, int v2, boolean front1, boolean front2, boolean back1, boolean back2){
        it1.no = bi(v1);
        it2.no = bi(v2);
        it1.front = front1;
        it2.front = front2;
        it1.end = back1;
        it2.end = back2;
        for (int i = 3; i <= k1; i++){
            State.merge(it1, it2, it3);
            State temp = it1;
            it1 = it2;
            it2 = it3;
            it3 = temp;
        }
        return it2.no;
    }

    public static BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
    public static StringTokenizer st = null;

    public static String nx() throws Exception {
        for (; st == null || !st.hasMoreTokens();) {
            String k1 = in.readLine();
            if (k1 == null) return null;
            st = new StringTokenizer(k1);
        }
        return st.nextToken();
    }

    public static int ni() throws Exception {
        return Integer.parseInt(nx());
    }

    public static long nl() throws Exception {
        return Long.parseLong(nx());
    }

    public static double nd() throws Exception {
        return Double.parseDouble(nx());
    }

    public static void px(Object... l1) {
        System.out.println(Arrays.deepToString(l1));
    }

    public static boolean FLUSH = false;
    public static PrintWriter out = new PrintWriter(System.out, FLUSH);

    public static void p(Object... l1) {
        for (int i = 0; i < l1.length; i++) {
            if (i != 0) out.print(' ');
            out.print(l1[i].toString());
        }
    }

    public static void pn(Object... l1) {
        for (int i = 0; i < l1.length; i++) {
            if (i != 0) out.print(' ');
            out.print(l1[i].toString());
        }
        out.println();
    }

    public static void pn(Collection l1) {
        boolean first = true;
        for (Object e : l1) {
            if (first) first = false;
            else out.print(' ');
            out.print(e.toString());
        }
        out.println();
    }

    private static BigInteger bi(long n1) {
        return BigInteger.valueOf(n1);
    }

}