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.FileReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.util.StringTokenizer;

public class NewYearLetter {
    public static void main(String[] args) throws Exception {
        InputReader r = new InputReader(System.in);
        int k = r.nextInt();
        int x = r.nextInt();
        n = r.nextInt();
        m = r.nextInt();
        char[] valid = { 'A', 'C', 'N' };
        for (char prefix1 : valid) {
            for (char prefix2 : valid) {
                for (char suffix1 : valid) {
                    for (char suffix2 : valid) {
                        if(n==1){
                            if(prefix1!=suffix1)
                                continue;
                        }
                        if(m==1){
                            if(prefix2!=suffix2)
                                continue;
                        }
                        for (int occ1 = 0; occ1 <= n / 2; occ1++) {
                            for (int occ2 = 0; occ2 <= m / 2; occ2++) {
                                long total = 0;
                                long s1 = occ1;
                                long s2 = occ2;
                                char start1 = prefix1;
                                char start2 = prefix2;
                                char end1 = suffix1;
                                char end2 = suffix2;
                                boolean can = true;
                                for (int index = 3; index <= k; index++) {
                                    if (total > x) {
                                        can = false;
                                        break;
                                    }
                                    long curr = s1 + s2;
                                    if (end1 == 'A' && start2 == 'C')
                                        curr++;
                                    total = curr;
                                    s1 = s2;
                                    s2 = curr;
                                    char start2T = start2;
                                    start2 = start1;
                                    start1 = start2T;
                                    end1 = end2;
                                }
                                if (can && total == x) {
                                    if (can1(0, occ1, prefix1, suffix1, 'N') && can2(0, occ2, prefix2, suffix2, 'N')) {
                                        get1(occ1, prefix1, suffix1, 'N');
                                        get2(occ2, prefix2, suffix2, 'N');
                                        return;
                                    }
                                }
                            }
                        }
                    }
                }
            }
        }
        System.out.println("Happy new year!");
    }

    private static void get1(int occ2, char p, char s, char c) {
        int index = 0;
        int occ = occ2;
        char prefix2 = p;
        char suffix2 = s;
        char prev = c;
        while(index<n){
            if (index == 0) {
                System.out.print(prefix2);
                prev = prefix2;
            } else if (index == n - 1) {
                System.out.print(suffix2);
                occ -= (prev == 'A' && suffix2 == 'C' ? 1 : 0);
                prev = suffix2;
            } else {
                if(can1(index + 1, occ, prefix2, suffix2, 'A')) {
                    System.out.print('A');
                    prev = 'A';
                }else if(can1(index + 1, occ - (prev == 'A' ? 1 : 0), prefix2, suffix2, 'C')) {
                    System.out.print('C');
                    occ -= (prev == 'A' ? 1 : 0);
                    prev = 'C';
                } else {
                    System.out.print('N');
                    prev = 'N';
                }
            }
            index++;
        }
        System.out.println();
    }

    private static void get2(int occ1, char p, char s, char c) {
        int index = 0;
        int occ = occ1;
        char prefix2 = p;
        char suffix2 = s;
        char prev = c;
        while(index<m){
            if (index == 0) {
                System.out.print(prefix2);
                prev = prefix2;
            } else if (index == m - 1) {
                System.out.print(suffix2);
                occ -= (prev == 'A' && suffix2 == 'C' ? 1 : 0);
                prev = suffix2;
            } else {
                if(can2(index + 1, occ, prefix2, suffix2, 'A')) {
                    System.out.print('A');
                    prev = 'A';
                }else if(can2(index + 1, occ - (prev == 'A' ? 1 : 0), prefix2, suffix2, 'C')) {
                    System.out.print('C');
                    occ -= (prev == 'A' ? 1 : 0);
                    prev = 'C';
                } else {
                    System.out.print('N');
                    prev = 'N';
                }
            }
            index++;
        }
        System.out.println();
    }

    static int n, m;
    static Boolean[][][][][] dp1 = new Boolean[101][55][4][4][4];
    static Boolean[][][][][] dp2 = new Boolean[101][55][4][4][4];
    private static boolean can1(int index, int occ2, char prefix2, char suffix2, char prev) {
        if (index == n) {
            if (occ2 == 0)
                return true;
            return false;
        }
        if (occ2 < 0)
            return false;
        if(dp1[index][occ2][c(prefix2)][c(suffix2)][c(prev)] != null)
            return dp1[index][occ2][c(prefix2)][c(suffix2)][c(prev)];
        boolean res = false;
        if (index == 0) {
            res |= can1(index + 1, occ2, prefix2, suffix2, prefix2);
        } else if (index == n - 1) {
            res |= can1(index + 1, occ2 - (prev == 'A' && suffix2 == 'C' ? 1 : 0), prefix2, suffix2, suffix2);
        } else {
            res |= can1(index + 1, occ2, prefix2, suffix2, 'A');
            res |= can1(index + 1, occ2 - (prev == 'A' ? 1 : 0), prefix2, suffix2, 'C');
            res |= can1(index + 1, occ2, prefix2, suffix2, 'N');
        }
        return dp1[index][occ2][c(prefix2)][c(suffix2)][c(prev)] = res;
    }

    private static boolean can2(int index, int occ2, char prefix2, char suffix2, char prev) {
        if (index == m) {
            if (occ2 == 0)
                return true;
            return false;
        }
        if (occ2 < 0)
            return false;
        if(dp2[index][occ2][c(prefix2)][c(suffix2)][c(prev)] != null)
            return dp2[index][occ2][c(prefix2)][c(suffix2)][c(prev)];
        boolean res = false;
        if (index == 0) {
            res |= can2(index + 1, occ2, prefix2, suffix2, prefix2);
        } else if (index == m - 1) {
            res |= can2(index + 1, occ2 - (prev == 'A' && suffix2 == 'C' ? 1 : 0), prefix2, suffix2, suffix2);
        } else {
            res |= can2(index + 1, occ2, prefix2, suffix2, 'A');
            res |= can2(index + 1, occ2 - (prev == 'A' ? 1 : 0), prefix2, suffix2, 'C');
            res |= can2(index + 1, occ2, prefix2, suffix2, 'N');
        }
        return dp2[index][occ2][c(prefix2)][c(suffix2)][c(prev)] = res;
    }
    
    static int c(char c){
        if(c=='A')
            return 0;
        if(c=='C')
            return 1;
        return 2;
    }

    static class InputReader {
        private BufferedReader reader;
        private StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream));
            tokenizer = null;
        }

        public InputReader(FileReader stream) {
            reader = new BufferedReader(stream);
            tokenizer = null;
        }

        public String nextLine() {
            try {
                return reader.readLine();
            } catch (IOException e) {
                // TODO Auto-generated catch block
                e.printStackTrace();
                return null;
            }
        }

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

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

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

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