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.*;

/**
 __                  __
 ( _)                ( _)
 / / \\              / /\_\_
 / /   \\            / / | \ \
 / /     \\          / /  |\ \ \
 /  /   ,  \ ,       / /   /|  \ \
 /  /    |\_ /|      / /   / \   \_\
 /  /  |\/ _ '_| \   / /   /   \    \\
 |  /   |/  0 \0\    / |    |    \    \\
 |    |\|      \_\_ /  /    |     \    \\
 |  | |/    \.\ o\o)  /      \     |    \\
 \    |     /\\`v-v  /        |    |     \\
 | \/    /_| \\_|  /         |    | \    \\
 | |    /__/_ `-` /   _____  |    |  \    \\
 \|    [__]  \_/  |_________  \   |   \    ()
 /    [___] (    \         \  |\ |   |   //
 |    [___]                  |\| \|   /  |/
 /|    [____]                  \  |/\ / / ||
 (  \   [____ /     ) _\      \  \    \| | ||
 \  \  [_____|    / /     __/    \   / / //
 |   \ [_____/   / /        \    |   \/ //
 |   /  '----|   /=\____   _/    |   / //
 __ /  /        |  /   ___/  _/\    \  | ||
 (/-(/-\)       /   \  (/\/\)/  |    /  | /
 (/\/\)           /   /   //
 _________/   /    /
 \____________/    (


 @author NTUDragons-Reborn
 */

public class C{
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        Task solver = new Task();
        solver.solve(in, out);
        out.close();
    }
    // main solver
    static class Task{

        double eps= 0.00000001;
        static final int MAXN = 10000001;

        // stores smallest prime factor for every number
        static int spf[] = new int[MAXN];

        Map<Integer,Set<Integer>> dp= new HashMap<>();

        // Calculating SPF (Smallest Prime Factor) for every
        // number till MAXN.
        // Time Complexity : O(nloglogn)
        public void sieve()
        {
            spf[1] = 1;
            for (int i=2; i<MAXN; i++)

                // marking smallest prime factor for every
                // number to be itself.
                spf[i] = i;

            // separately marking spf for every even
            // number as 2
            for (int i=4; i<MAXN; i+=2)
                spf[i] = 2;

            for (int i=3; i*i<MAXN; i++)
            {
                // checking if i is prime
                if (spf[i] == i)
                {
                    // marking SPF for all numbers divisible by i
                    for (int j=i*i; j<MAXN; j+=i)

                        // marking spf[j] if it is not
                        // previously marked
                        if (spf[j]==j)
                            spf[j] = i;
                }
            }
        }

        // A O(log n) function returning primefactorization
        // by dividing by smallest prime factor at every step
        public Set<Integer> getFactorization(int x)
        {
            if(dp.containsKey(x)) return dp.get(x);
            Set<Integer> ret = new HashSet<>();
            while (x != 1)
            {
                if(spf[x]!=2) ret.add(spf[x]);
                x = x / spf[x];
            }
            dp.put(x,ret);
            return ret;
        }
        // function to find first index >= x
        public int lowerIndex(List<Integer> arr, int n, int x)
        {
            int l = 0, h = n - 1;
            while (l <= h)
            {
                int mid = (l + h) / 2;
                if (arr.get(mid) >= x)
                    h = mid - 1;
                else
                    l = mid + 1;
            }
            return l;
        }

        // function to find last index <= y
        public int upperIndex(List<Integer> arr, int n, int y)
        {
            int l = 0, h = n - 1;
            while (l <= h)
            {
                int mid = (l + h) / 2;
                if (arr.get(mid) <= y)
                    l = mid + 1;
                else
                    h = mid - 1;
            }
            return h;
        }

        // function to count elements within given range
        public int countInRange(List<Integer> arr, int n, int x, int y)
        {
            // initialize result
            int count = 0;
            count = upperIndex(arr, n, y) -
                    lowerIndex(arr, n, x) + 1;
            return count;
        }
        InputReader in;
        PrintWriter out;
        int k,x,n,m;
        public void solve(InputReader in, PrintWriter out) {
            this.in=in;
            this.out=out;
            k= in.nextInt(); x= in.nextInt(); n= in.nextInt(); m= in.nextInt();
            for(char a='A';a<='C';a++){
                for(char b='A';b<='C';b++){
                    for(char c='A';c<='C';c++){
                        for(char d='A';d<='C';d++){
                            for(int cnt1=0; cnt1<=n/2;cnt1++){
                                for(int cnt2=0; cnt2<=m/2;cnt2++){
                                    if(check(a,b,cnt1,c,d,cnt2)) return;
                                }
                            }
                        }
                    }
                }
            } 
            out.println("Happy new year!");
        }
        public boolean check(char a, char b, int cnt1, char c, char d, int cnt2){
            String s1="", s2="";
            int cnt=0;
            if(!checkMake(a,b,cnt1,n)) return false;
            if(!checkMake(c,d,cnt2,m)) return false;

            long[] f= new long[100];
            char[] start= new char[100], finish= new char[100];

            f[1]= cnt1;
            start[1]=a;
            finish[1]=b;

            f[2]= cnt2;
            start[2] = c;
            finish[2] = d;

            for (int i = 3; i <= k; i++) {
                f[i] = f[i - 2] + f[i - 1];
                if (f[i] > x) return false;
                start[i] = start[i - 2];
                finish[i] = finish[i - 1];
                f[i] += (finish[i - 2] == 'A' && start[i - 1] == 'C')?1:0;
            }

            if (f[k] != x) return false;

            s1 = make(a, b, cnt1, n);
            s2 = make(c, d, cnt2, m);
            out.println(s1);
            out.println(s2);

            return true;

        }
        public boolean checkMake(char start, char finish, int cnt, int len){
            if(len==1 && start!=finish) return false;
            if(len==1 && start== finish && cnt==0) return true;

            len-= 1+ 2*cnt;
            if(cnt!=0 && start=='A') len++;
            if(len<0) return false;
            return (finish=='C' ||  len>0);
        }
        public String make(char start, char finish, int cnt, int len){
            String s=start+"";
            if(cnt>0 && start=='A') {
                s+='C'; cnt--;
            }
            for(int i=0;i<cnt;i++) s+= "AC";
            if(s.length()>len) return "";
            while(s.length()<(len-1)) s+="B";
            if(s.length()<len) s+=finish;
            if(s.charAt(len-1)!=finish) return "";
            return s;
        }

        // private int cal()
        public static boolean nextPermutation(char[] array){
            boolean hasNext = false;
            int i;
            for(i = array.length-2; i >= 0; i--){
                if(array[i] < array[i+1]){
                    hasNext = true;
                    break;
                }
            }
             
            if(!hasNext){// If all elements are arranged from largest to smallest, it means the largest string
                return false;
            }
             
            // Find backward from the subscript of i + 1 (must be monotonically decreasing), find a smallest element in the set larger than array [i]
            int j;
            for(j = i+1; j < array.length; j++){
                if(array[j] <= array[i]){
                    break;
                }
            }
            j--;
             
            // Swap these two elements, and then reverse all the elements in i + 1 and later (i + 1, array.length)
            swap(array, i, j);
            reverse(array, i+1, array.length);
       
            return true;
        }
        public static void swap(char[] array, int i, int j) {
            char temp =array[i];
            array[i] = array[j];
            array[j] =temp;	
        }
        public static void reverse(char[] array, int start, int end){
            for(int i = start, j = end-1; i < j; i++, j--) {
                swap(array, i, j);
            }
        }

        public static class compareL implements Comparator<Tuple>{
            @Override
            public int compare(Tuple t1, Tuple t2) {
                return t2.l - t1.l;
            }
        }
        public static class compareR implements Comparator<Tuple>{
            @Override
            public int compare(Tuple t1, Tuple t2) {
                return t1.r - t2.r;
            }
        }
        public static class Tuple{
            public int l, r, w;
            public Tuple(int l, int r,int w){
                this.l = l; this.r= r;
                this.w =w;
            }
        }
        public static class Range implements Comparable<Range>{
            public int l, r;
            List<Integer> data;
            int weight;
            public Range(int l, int r, List<Integer> data){
                this.data = data;
                this.l = l; this.r =r;
                this.weight = (int)1e9;
            }

            @Override
            public int compareTo(Range o) {
                return this.l - o.l;
            }
        }
        public int _gcd(int a,  int  b)
        {

            if(b == 0) {
                return a;
            }
            else {
                return _gcd(b, a % b);
            }
        }

    }

    static class Tuple implements Comparable<Tuple>{
        int x, y, z;
        public Tuple(int x, int y, int z){
            this.x= x;
            this.y= y;
            this.z=z;
        }
        @Override
        public int compareTo(Tuple o){
            return this.x-o.x;
        }
    }

    static class Pair implements Comparable<Pair>{
        public int x;
        public int y;
        public Pair(int x, int y){
            this.x= x;
            this.y= y;
        }

        @Override
        public int compareTo(Pair o) {
            return this.x-o.x;
        }
    }
    // fast input reader class;
    static class InputReader {
        BufferedReader br;
        StringTokenizer st;

        public InputReader(InputStream stream) {
            br = new BufferedReader(new InputStreamReader(stream));
        }

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

        public int nextInt() {
            return Integer.parseInt(nextToken());
        }
        public double nextDouble(){
            return Double.parseDouble(nextToken());
        }
        public long nextLong(){
            return Long.parseLong(nextToken());
        }
    }
}