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.io.*;
import java.awt.Point;
import java.math.BigDecimal;
import java.math.BigInteger;

import static java.lang.Math.*;

// Solution is at the bottom of code

public class NewYear_D implements Runnable{
	
	static Random random;
	
	static {
		random = new Random();
	}
	
	final boolean ONLINE_JUDGE = System.getProperty("ONLINE_JUDGE") != null;
	
	BufferedReader in;
	OutputWriter out;
	StringTokenizer tok = new StringTokenizer("");
	
	public static void main(String[] args){
		new Thread(null, new NewYear_D(), "", 128 * (1L << 20)).start();
	}
	
	/////////////////////////////////////////////////////////////////////
	
	void init() throws FileNotFoundException{
		Locale.setDefault(Locale.US);
		
		if (ONLINE_JUDGE){
			in = new BufferedReader(new InputStreamReader(System.in));
			out = new OutputWriter(System.out);
		}else{
			in = new BufferedReader(new FileReader("input.txt"));
			out = new OutputWriter("output.txt");
		}
	}
	
	////////////////////////////////////////////////////////////////
	
	long timeBegin, timeEnd;

	void time(){
		timeEnd = System.currentTimeMillis();
		System.err.println("Time = " + (timeEnd - timeBegin));
	}
	
	void debug(Object... objects){
		if (ONLINE_JUDGE){
			for (Object o: objects){
				System.err.println(o.toString());
			}
		}
	}
	
	/////////////////////////////////////////////////////////////////////
	
	public void run(){
		try{
			timeBegin = System.currentTimeMillis();
			Locale.setDefault(Locale.US);
			
			init();
			
//			for (int n = 1; n <= 100; ++n) {
//				for (int m = 1; m <= 100; ++m) {
//					for (int k = 3; k <= 50; ++k) {
//						for (int it = 0; it < 100; ++it) {
//							long x = random.nextInt(1000 * 1000 * 1000 + 1);
//							solve(k, x, n, m)
//						}
//					}
//				}
//			}
			solve();
			
			out.close();
			time();
		}catch (Exception e){
			e.printStackTrace(System.err);
			System.exit(-1);
		}
	}
	
	/////////////////////////////////////////////////////////////////////
	
	String delim = " ";
	
	String readString() throws IOException{
		while(!tok.hasMoreTokens()){
			try{
				tok = new StringTokenizer(in.readLine());
			}catch (Exception e){
				return null;
			}
		}
		
		return tok.nextToken(delim);
	}
	
	String readLine() throws IOException{
		return in.readLine();
	}
	
	/////////////////////////////////////////////////////////////////
	
	final char NOT_A_SYMBOL = '\0';
	
	char readChar() throws IOException{
		int intValue = in.read();
		
		if (intValue == -1){
			return NOT_A_SYMBOL;
		}
		
		return (char) intValue;
	}
	
	char[] readCharArray() throws IOException{
		return readLine().toCharArray();
	}
	
	/////////////////////////////////////////////////////////////////
	
	int readInt() throws IOException{
		return Integer.parseInt(readString());
	}
	
	int[] readIntArray(int size) throws IOException{
		int[] array = new int[size];
		
		for (int index = 0; index < size; ++index){
			array[index] = readInt();
		}
		
		return array;
	}
	
	///////////////////////////////////////////////////////////////////
	
	long readLong() throws IOException{
		return Long.parseLong(readString());
	}
	
	long[] readLongArray(int size) throws IOException{
		long[] array = new long[size];
		
		for (int index = 0; index < size; ++index){
			array[index] = readLong();
		}
		
		return array;
	}
	
	////////////////////////////////////////////////////////////////////
	
	double readDouble() throws IOException{
		return Double.parseDouble(readString());
	}
	
	double[] readDoubleArray(int size) throws IOException{
		double[] array = new double[size];
		
		for (int index = 0; index < size; ++index){
			array[index] = readDouble();
		}
		
		return array;
	}
	
	////////////////////////////////////////////////////////////////////
		
	BigInteger readBigInteger() throws IOException {
		return new BigInteger(readString());
	}
	
	BigDecimal readBigDecimal() throws IOException {
		return new BigDecimal(readString());
	}
	
	/////////////////////////////////////////////////////////////////////
	
	Point readPoint() throws IOException{
		int x = readInt();
		int y = readInt();
		return new Point(x, y);
	}
	
	Point[] readPointArray(int size) throws IOException{
		Point[] array = new Point[size];
		
		for (int index = 0; index < size; ++index){
			array[index] = readPoint();
		}
		
		return array;
	}
	
	/////////////////////////////////////////////////////////////////////
	
	List<Integer>[] readGraph(int vertexNumber, int edgeNumber)
	throws IOException{
		@SuppressWarnings("unchecked")
		List<Integer>[] graph = new List[vertexNumber];
		
		for (int index = 0; index < vertexNumber; ++index){
			graph[index] = new ArrayList<Integer>();
		}
		
		while (edgeNumber-- > 0){
			int from = readInt() - 1;
			int to = readInt() - 1;
			
			graph[from].add(to);
			graph[to].add(from);
		}
		
		return graph;
	}
	
	/////////////////////////////////////////////////////////////////////
	
	class OutputWriter extends PrintWriter{

		final int DEFAULT_PRECISION = 12;
		
		int precision;
		String format, formatWithSpace;
		
		{
			precision = DEFAULT_PRECISION;
			
			format = createFormat(precision);
			formatWithSpace = format + " ";
		}
		
		public OutputWriter(OutputStream out) {
			super(out);
		}

		public OutputWriter(String fileName) throws FileNotFoundException {
			super(fileName);
		}
		
		public int getPrecision() {
			return precision;
		}

		public void setPrecision(int precision) {
			precision = max(0, precision);
			this.precision = precision;
			
			format = createFormat(precision);
			formatWithSpace = format + " ";
		}
		
		private String createFormat(int precision){
			return "%." + precision + "f";
		}
		
		@Override
		public void print(double d){
			printf(format, d);
		}
		
		public void printWithSpace(double d){
			printf(formatWithSpace, d);
		}

		public void printAll(double...d){
			for (int i = 0; i < d.length - 1; ++i){
				printWithSpace(d[i]);
			}
			
			print(d[d.length - 1]);
		}
		
		@Override
		public void println(double d){
			printlnAll(d);
		}
		
		public void printlnAll(double... d){
			printAll(d);
			println();
		}
	}
	
	/////////////////////////////////////////////////////////////////////
	
	int[][] steps = {{-1, 0}, {1, 0}, {0, -1}, {0, 1}}; 
	int[][] steps8 = {
			{-1, 0}, {1, 0}, {0, -1}, {0, 1},
			{-1, -1}, {1, 1}, {1, -1}, {-1, 1}
	};
	
	boolean check(int index, int lim){
		return (0 <= index && index < lim);
	}
	
	/////////////////////////////////////////////////////////////////////
	
	boolean checkBit(int mask, int bitNumber){
		return (mask & (1 << bitNumber)) != 0;
	}
	
	/////////////////////////////////////////////////////////////////////
	
	void solve() throws IOException{
		int k = readInt();
		long x = readLong();
		
		int n = readInt();
		int m = readInt();
		
		long[] count = new long[k];
		int[] masks = new int[k];
		
		for (int firstCount = 0; firstCount * 2 <= n; ++firstCount) {
			count[0] = firstCount;
			
			for (int firstMask = 0; firstMask < 9; ++firstMask) {
				masks[0] = firstMask;
				
				if (n == 1 && firstMask % 3 != firstMask / 3) {
					continue;
				}
				
				if (n % 2 == 0 && firstCount * 2 == n && firstMask != (0 * 3 + 1 * 1)) continue; // all string == ACACACAC...
				if (n > 1 && n % 2 == 1 && firstCount * 2 == n - 1 && (firstMask / 3 != 0 && firstMask % 3 != 1)) continue; // or XACACACAC, or ACACACAC...X
				if (n == 2 && firstMask == 1 && firstCount != 1) continue;
				
				for (int secondCount = 0; secondCount * 2 <= m; ++secondCount) {
					count[1] = secondCount;
					
					for (int secondMask = 0; secondMask < 9; ++secondMask) {
						masks[1] = secondMask;
						
						if (masks[0] == 1 && masks[1] == 3) {
							masks[0] = 1;
						}
						
						if (m == 1 && secondMask % 3 != secondMask / 3) {
							continue;
						}
						
						if (m % 2 == 0 && secondCount * 2 == m && secondMask != (0 * 3 + 1 * 1)) continue; // all string == ACACACAC...
						if (m > 1 && m % 2 == 1 && secondCount * 2 == m - 1 && (secondMask / 3 != 0 && secondMask % 3 != 1)) continue; // or XACACACAC, or ACACACAC...X
						if (m == 2 && secondMask == 1 && secondCount != 1) continue;
						
						for (int i = 2; i < k; ++i) {
							count[i] = count[i-2] + count[i-1];
							
							if (masks[i-2] % 3 == 0 && masks[i-1] / 3 == 1) {
								count[i]++;
							}
							
							masks[i] = (masks[i-2] / 3 * 3) + (masks[i-1] % 3);
							
							if (count[i] > x) {
								count[k-1] = -1;
								break;
							}
						}
						
						if (count[k-1] == x) {
							printString(n, firstCount, firstMask);
							printString(m, secondCount, secondMask);
							
							return;
						}
					}
				}
			}
		}
		
		out.println("Happy new year!");
	}
	
	void printString(int length, long count, int mask) {
		boolean firstA = false;
		int curLength = 0;
		
		if (mask / 3 == 0) {
			firstA = true;
			out.print("A");
		} else if (mask / 3 == 1) {
			out.print("C");
		} else {
			out.print("X");
		}
		
		curLength++;
		
		while (count> 0) {
			if (firstA) {
				out.print("C");
				curLength++;
				firstA = false;
				
			} else {
				out.print("AC");
				curLength += 2;
			}
			
			count--;
		}
		
		while (curLength < length - 1) {
			out.print("X");
			curLength++;
		}
		
		if (curLength < length) {
			if (mask % 3 == 0) {
				out.print("A");
			} else if (mask % 3 == 1) {
				out.print("C");
			} else {
				out.print("X");
			}
			
			curLength++;
		}
		
		out.println();
		
		if (curLength != length) throw new RuntimeException();
	}
}