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.File;
import java.io.FileNotFoundException;
import java.io.FileOutputStream;
import java.io.FileReader;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashMap;
import java.util.HashSet;
import java.util.LinkedList;
import java.util.PriorityQueue;
import java.util.StringTokenizer;
import java.util.TreeMap;
import java.util.TreeSet;

/**
 * 4 4
 * 1 5 3 4
 * 1 2
 * 1 3
 * 2 3
 * 3 3
 *
 *
 * @author pttrung
 */
public class A {

    public static long Mod = (long) (1e9);
    public static long[][] dp, dp2;

    public static void main(String[] args) throws FileNotFoundException {

        //PrintWriter out = new PrintWriter(new FileOutputStream(new File("output.txt")));
        PrintWriter out = new PrintWriter(System.out);
        Scanner in = new Scanner();
        int k = in.nextInt();
        int x = in.nextInt();
        int n = in.nextInt();
        int m = in.nextInt();
        dp = new long[k + 1][2];
        dp2 = new long[k + 1][5];
        for (long[] a : dp) {
            Arrays.fill(a, -1);
        }
        for (long[] a : dp2) {
            Arrays.fill(a, -1);
        }
        long[] res = cal(k);
        long[] res1 = cal2(k);
        //System.out.println(res[0] + " " + res[1]);
       // System.out.println(Arrays.toString(res1));
        boolean ok = false;
        for (long i = 0; i * 2 <= n && !ok; i++) {
            for (long j = 0; j * 2 <= m; j++) {

                long tmp = i * res[0] + j * res[1];
                // System.out.println(i + " " + j + " " + tmp);
                if (tmp == x) {
                    ok = true;
                    for (int q = 0; q < i * 2; q += 2) {
                        out.print("AC");
                    }
                    if (i * 2 < n) {
                        for (long q = i * 2; q < n; q++) {
                            out.print("Z");
                        }
                    }
                    out.println();
                    for (int q = 0; q < j * 2; q += 2) {
                        out.print("AC");
                    }
                    if (i * 2 < m) {
                        for (long q = j * 2; q < m; q++) {
                            out.print("A");
                        }
                    }
                    out.println();
                    break;
                } else {
                    long a = n - 2 * i;
                    long b = m - 2 * j;
                    if (b > 1) {
                        if (tmp + res1[4] == x) {
                            ok = true;
                            for (int q = 0; q < i * 2; q += 2) {
                                out.print("AC");
                            }
                            if (i * 2 < n) {
                                for (long q = i * 2; q < n; q++) {
                                    out.print("Z");
                                }
                            }
                            out.println();
                            out.print("C");
                            for (int q = 0; q < j * 2; q += 2) {
                                out.print("AC");
                            }
                            for (long q = 2 * j + 1; q < m; q++) {
                                out.print("A");
                            }
                            out.println();
                            break;
                        }
                    }

                    if (a > 0 && b > 0) {
                        if (tmp + res1[2] == x) {
                            ok = true;
                            for (int q = 0; q < i * 2; q += 2) {
                                out.print("AC");
                            }
                            if (i * 2 < n) {
                                for (long q = i * 2; q < n; q++) {
                                    out.print("A");
                                }
                            }
                            out.println();
                            out.print("C");
                            for (int q = 0; q < j * 2; q += 2) {
                                out.print("AC");
                            }
                            for (long q = 2 * j + 1; q < m; q++) {
                                out.print("C");
                            }
                            out.println();
                            break;
                        }


                        if (tmp + res1[3] == x) {
                            ok = true;
                            out.print("C");
                            for (int q = 0; q < i * 2; q += 2) {
                                out.print("AC");
                            }
                            if (i * 2 < n) {
                                for (long q = i * 2 + 1; q < n; q++) {
                                    out.print("C");
                                }
                            }
                            out.println();
                            // out.print("C");
                            for (int q = 0; q < j * 2; q += 2) {
                                out.print("AC");
                            }
                            for (long q = 2 * j; q < m; q++) {
                                out.print("A");
                            }
                            out.println();
                            break;
                        }

                    }
                    if (a > 1 && b > 1) {
                        if (tmp + res1[2] + res1[3] + res1[4] == x) {
                            ok = true;
                            out.print("C");
                            for (int q = 0; q < i * 2; q += 2) {
                                out.print("AC");
                            }
                            if (i * 2 < n) {
                                for (long q = i * 2 + 1; q < n; q++) {
                                    out.print("A");
                                }
                            }
                            out.println();
                            out.print("C");
                            for (int q = 0; q < j * 2; q += 2) {
                                out.print("AC");
                            }
                            for (long q = 2 * j + 1; q < m; q++) {
                                out.print("A");
                            }
                            out.println();
                            break;
                        }
                    }
                }

            }
        }
        if (!ok) {
            out.println("Happy new year!");
        }

        out.close();
    }

    static long[] cal2(int k) {
        if (k == 1) {
            return new long[]{0, 0, 0, 0, 0};
        }
        if (k == 2) {
            return new long[]{1, 1, 0, 0, 0};
        }
        if (dp2[k][0] != -1) {
            return dp2[k];
        }
        long[] a = cal2(k - 2);
        long[] b = cal2(k - 1);
        long[] result = new long[5];
        result[2] += a[2] + b[2];
        result[3] += a[3] + b[3];
        result[4] += a[4] + b[4];
        if ((a[1] == 0 && b[0] == 1)) {// 12
            result[2]++;
        } else if (a[1] == 1 && b[0] == 0) {//21
            result[3]++;
        } else if (a[1] == 1 && b[0] == 1) {//22
            result[4]++;
        }
        result[0] = a[0];
        result[1] = b[1];
        dp2[k] = result;
        return result;
    }

    static long[] cal(int k) {
        if (k == 1) {
            return new long[]{1, 0};
        }
        if (k == 2) {
            return new long[]{0, 1};
        }
        if (dp[k][0] != -1) {
            return dp[k];
        }
        long[] result = new long[2];
        long[] a = cal(k - 2);
        long[] b = cal(k - 1);
        result[0] = a[0] + b[0];
        result[1] = a[1] + b[1];
        return dp[k] = result;
    }

    static long dist2(long x1, long y1, long z1, long x2, long y2, long z2) {
        long x = x1 - x2;
        long y = y1 - y2;
        long z = z1 - z2;
        return x * x + y * y + z * z;
    }

    static int find(int index, int[] u) {
        if (index != u[index]) {
            return u[index] = find(u[index], u);
        }
        return index;
    }

    public static long pow(int a, int b, long mod) {
        if (b == 0) {
            return 1;
        }
        if (b == 1) {
            return a;
        }
        long v = pow(a, b / 2, mod);
        if (b % 2 == 0) {
            return (v * v) % mod;
        } else {
            return (((v * v) % mod) * a) % mod;
        }
    }

    public static int[][] powSquareMatrix(int[][] A, long p) {
        int[][] unit = new int[A.length][A.length];
        for (int i = 0; i < unit.length; i++) {
            unit[i][i] = 1;
        }
        if (p == 0) {
            return unit;
        }
        int[][] val = powSquareMatrix(A, p / 2);
        if (p % 2 == 0) {
            return mulMatrix(val, val);
        } else {
            return mulMatrix(A, mulMatrix(val, val));
        }

    }

    public static int[][] mulMatrix(int[][] A, int[][] B) {
        int[][] result = new int[A.length][B[0].length];
        for (int i = 0; i < result.length; i++) {
            for (int j = 0; j < result[0].length; j++) {
                long temp = 0;
                for (int k = 0; k < A[0].length; k++) {

                    temp += ((long) A[i][k] * B[k][j] % Mod);
                    temp %= Mod;
                }
                temp %= Mod;
                result[i][j] = (int) temp;
            }
        }

        return result;
    }

    public static boolean nextPer(int[] data) {
        int i = data.length - 1;
        while (i > 0 && data[i] < data[i - 1]) {
            i--;
        }
        if (i == 0) {
            return false;
        }
        int j = data.length - 1;
        while (data[j] < data[i - 1]) {
            j--;
        }
        int temp = data[i - 1];
        data[i - 1] = data[j];
        data[j] = temp;
        Arrays.sort(data, i, data.length);
        return true;




    }

    static class FT {

        int[] data;

        FT(int n) {
            data = new int[n];
        }

        void update(int index, int val) {
            // System.out.println("UPDATE INDEX " + index);
            while (index < data.length) {
                data[index] += val;
                index += index & (-index);

                //    System.out.println("NEXT " +index);
            }
        }

        int get(int index) {
            //  System.out.println("GET INDEX " + index);
            int result = 0;
            while (index > 0) {
                result += data[index];
                index -= index & (-index);
                // System.out.println("BACK " + index);
            }
            return result;
        }
    }

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

    static long pow(long a, int b) {
        if (b == 0) {
            return 1;
        }
        if (b == 1) {
            return a;
        }
        long val = pow(a, b / 2);
        if (b % 2 == 0) {

            return val * val % Mod;
        } else {
            return (val * val % Mod) * a % Mod;
        }
    }

//    static Point intersect(Point a, Point b, Point c) {
//        double D = cross(a, b);
//        if (D != 0) {
//            return new Point(cross(c, b) / D, cross(a, c) / D);
//        }
//        return null;
//    }
//
//    static Point convert(Point a, double angle) {
//        double x = a.x * cos(angle) - a.y * sin(angle);
//        double y = a.x * sin(angle) + a.y * cos(angle);
//        return new Point(x, y);
//    }
    static Point minus(Point a, Point b) {
        return new Point(a.x - b.x, a.y - b.y);
    }
//
//    static Point add(Point a, Point b) {
//        return new Point(a.x + b.x, a.y + b.y);
//    }
//

    /**
     * Cross product ab*ac
     *
     * @param a
     * @param b
     * @param c
     * @return
     */
    static double cross(Point a, Point b, Point c) {
        Point ab = new Point(b.x - a.x, b.y - a.y);
        Point ac = new Point(c.x - a.x, c.y - a.y);
        return cross(ab, ac);
    }

    static double cross(Point a, Point b) {
        return a.x * b.y - a.y * b.x;
    }

    /**
     * Dot product ab*ac;
     *
     * @param a
     * @param b
     * @param c
     * @return
     */
    static long dot(Point a, Point b, Point c) {
        Point ab = new Point(b.x - a.x, b.y - a.y);
        Point ac = new Point(c.x - a.x, c.y - a.y);
        return dot(ab, ac);
    }

    static long dot(Point a, Point b) {
        long total = a.x * b.x;
        total += a.y * b.y;
        return total;
    }

    static double dist(Point a, Point b) {
        long total = (a.x - b.x) * (a.x - b.x) + (a.y - b.y) * (a.y - b.y);
        return Math.sqrt(total);
    }

    static long norm(Point a) {
        long result = a.x * a.x;
        result += a.y * a.y;
        return result;
    }

    static double dist(Point a, Point b, Point x, boolean isSegment) {
        double dist = cross(a, b, x) / dist(a, b);
        // System.out.println("DIST " + dist);

        if (isSegment) {
            Point ab = new Point(b.x - a.x, b.y - a.y);

            long dot1 = dot(a, b, x);
            long norm = norm(ab);
            double u = (double) dot1 / norm;
            if (u < 0) {
                return dist(a, x);
            }

            if (u > 1) {
                return dist(b, x);
            }
        }
        return Math.abs(dist);




    }

    static long squareDist(Point a, Point b) {
        long x = a.x - b.x;
        long y = a.y - b.y;
        return x * x + y * y;
    }

    static class Point {

        int x, y;

        public Point(int x, int y) {
            this.x = x;
            this.y = y;
        }

        @Override
        public String toString() {
            return "Point{" + "x=" + x + ", y=" + y + '}';
        }
    }

    static class Scanner {

        BufferedReader br;
        StringTokenizer st;

        public Scanner() throws FileNotFoundException {
            //System.setOut(new PrintStream(new BufferedOutputStream(System.out), true));
            br = new BufferedReader(new InputStreamReader(System.in));
            //br = new BufferedReader(new FileReader(new File("A-large (2).in")));
        }

        public String next() {


            while (st == null || !st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (Exception e) {
                    throw new RuntimeException();
                }
            }
            return st.nextToken();
        }

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

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

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

        public String nextLine() {
            st = null;
            try {
                return br.readLine();
            } catch (Exception e) {
                throw new RuntimeException();
            }
        }

        public boolean endLine() {
            try {
                String next = br.readLine();
                while (next != null && next.trim().isEmpty()) {
                    next = br.readLine();
                }
                if (next == null) {
                    return true;
                }
                st = new StringTokenizer(next);
                return st.hasMoreTokens();
            } catch (Exception e) {
                throw new RuntimeException();
            }
        }
    }
}