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.BufferedReader;
import java.io.BufferedWriter;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.util.ArrayList;
import java.util.List;
import java.util.StringTokenizer;

public class _379D {

  static int k, n, m;
  static long x;

  static class State {
    boolean aLast;
    boolean cFirst;
    long cnt;

    public State() {

    }

    public State(boolean cFirst, boolean aLast, long cnt) {
      this.aLast = aLast;
      this.cFirst = cFirst;
      this.cnt = cnt;
      this.cnt = Math.min(this.cnt, 10000000000L);
    }

    public State add(State other) {
      return new State(cFirst, other.aLast, cnt + other.cnt + (aLast && other.cFirst ? 1 : 0));
    }

    @Override
    public String toString() {
      return String.format("%s %s %d", cFirst, aLast, cnt);
    }

    public String toString(int len) {
      StringBuilder builder = new StringBuilder();

      int cb = 0;
      if (cFirst) {
        builder.append('C');
        cb++;
      }
      for (int i = 0; i < cnt; i++) {
        builder.append('A');
        builder.append('C');
        cb += 2;
      }
      for (; cb < len; cb++)
        builder.append('D');

      char[] ans = builder.toString().toCharArray();
      if (aLast)
        ans[ans.length - 1] = 'A';

      return String.valueOf(ans);
    }
  }

  public static List<State> gen(int cnt, int len) {
    List<State> list = new ArrayList<>();
    list.add(new State(false, false, cnt));
    if (2 * cnt < len) {
      list.add(new State(true, false, cnt));
      list.add(new State(false, true, cnt));
    }
    if (2 * cnt + 1 < len) {
      list.add(new State(true, true, cnt));
    }
    return list;
  }

  public static void main(String[] args) throws Exception {
    Reader.init(System.in);
    BufferedWriter cout = new BufferedWriter(new OutputStreamWriter(System.out));

    k = Reader.nextInt();
    x = Long.parseLong(Reader.next());
    n = Reader.nextInt();
    m = Reader.nextInt();

    boolean good = false;
    loop: {
      for (int i = 0; i <= n / 2; i++)
        for (int j = 0; j <= m / 2; j++)
          for (State cb : gen(i, n))
            for (State wb : gen(j, m)) {
              State[] f = new State[k];
              f[0] = cb;
              f[1] = wb;
              for (int l = 2; l < f.length; l++)
                f[l] = f[l - 2].add(f[l - 1]);

              if (f[k - 1].cnt == x) {
                good = true;
                System.out.println(f[0].toString(n));
                System.out.println(f[1].toString(m));
                break loop;
              }
            }

    }
    if (!good)
      System.out.println("Happy new year!");
    cout.close();
  }

  static class Pair<U extends Comparable<U>, V extends Comparable<V>> implements Comparable<Pair<U, V>> {
    final U _1;
    final V _2;

    private Pair(U key, V val) {
      this._1 = key;
      this._2 = val;
    }

    public static <U extends Comparable<U>, V extends Comparable<V>> Pair<U, V> instanceOf(U _1, V _2) {
      return new Pair<U, V>(_1, _2);
    }

    @Override
    public String toString() {
      return _1 + " " + _2;
    }

    @Override
    public int hashCode() {
      int res = 17;
      res = res * 31 + _1.hashCode();
      res = res * 31 + _2.hashCode();
      return res;
    }

    @Override
    public int compareTo(Pair<U, V> that) {
      int res = this._1.compareTo(that._1);
      if (res < 0 || res > 0)
        return res;
      else
        return this._2.compareTo(that._2);
    }

    @Override
    public boolean equals(Object obj) {
      if (this == obj)
        return true;
      if (!(obj instanceof Pair))
        return false;
      Pair<?, ?> that = (Pair<?, ?>) obj;
      return _1.equals(that._1) && _2.equals(that._2);
    }
  }

  /** Class for buffered reading int and double values */
  static class Reader {
    static BufferedReader reader;
    static StringTokenizer tokenizer;

    /** call this method to initialize reader for InputStream */
    static void init(InputStream input) {
      reader = new BufferedReader(new InputStreamReader(input));
      tokenizer = new StringTokenizer("");
    }

    /** get next word */
    static String next() throws IOException {
      while (!tokenizer.hasMoreTokens()) {
        // TODO add check for eof if necessary
        tokenizer = new StringTokenizer(reader.readLine());
      }
      return tokenizer.nextToken();
    }

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

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

  static class ArrayUtil {
    static void swap(int[] a, int i, int j) {
      int tmp = a[i];
      a[i] = a[j];
      a[j] = tmp;
    }

    static void swap(long[] a, int i, int j) {
      long tmp = a[i];
      a[i] = a[j];
      a[j] = tmp;
    }

    static void swap(double[] a, int i, int j) {
      double tmp = a[i];
      a[i] = a[j];
      a[j] = tmp;
    }

    static void swap(char[] a, int i, int j) {
      char tmp = a[i];
      a[i] = a[j];
      a[j] = tmp;
    }

    static void swap(boolean[] a, int i, int j) {
      boolean tmp = a[i];
      a[i] = a[j];
      a[j] = tmp;
    }

    static void reverse(int[] a, int i, int j) {
      for (; i < j; i++, j--)
        swap(a, i, j);
    }

    static void reverse(long[] a, int i, int j) {
      for (; i < j; i++, j--)
        swap(a, i, j);
    }

    static void reverse(double[] a, int i, int j) {
      for (; i < j; i++, j--)
        swap(a, i, j);
    }

    static void reverse(char[] a, int i, int j) {
      for (; i < j; i++, j--)
        swap(a, i, j);
    }

    static void reverse(boolean[] a, int i, int j) {
      for (; i < j; i++, j--)
        swap(a, i, j);
    }

    static long sum(int[] a) {
      int sum = 0;
      for (int i : a)
        sum += i;
      return sum;
    }

    static long sum(long[] a) {
      long sum = 0;
      for (long i : a)
        sum += i;
      return sum;
    }

    static double sum(double[] a) {
      double sum = 0;
      for (double i : a)
        sum += i;
      return sum;
    }

    static int max(int[] a) {
      int max = Integer.MIN_VALUE;
      for (int i : a)
        if (i > max)
          max = i;
      return max;
    }

    static int min(int[] a) {
      int min = Integer.MAX_VALUE;
      for (int i : a)
        if (i < min)
          min = i;
      return min;
    }

    static long max(long[] a) {
      long max = Long.MIN_VALUE;
      for (long i : a)
        if (i > max)
          max = i;
      return max;
    }

    static long min(long[] a) {
      long min = Long.MAX_VALUE;
      for (long i : a)
        if (i < min)
          min = i;
      return min;
    }
  }
}