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.math.*;
import java.util.*;


import static java.util.Arrays.*;

public class D {
	private static final int mod = (int)1e9+7;

	final Random random = new Random(0);
	final IOFast io = new IOFast();
	
//	long[][][][][][][] dp = new long[50][3][3][3][3][51][51];
	
	long func(int k, int p1, int s1, int p2, int s2, long v1, long v2) {
		/*
		if(dp[k][p1][s1][p2][s2][a][b] == -1) {
			long ans = func(k - 1, p1, s1, p2, s2, a, b);
		}
		
		return dp[k][p1][s1][p2][s2][a][b];
		*/
		
		if(k == 0) return v2;

		int p3 = p1;
		int s3 = s2;
		long v3 = v1 + v2 + (s1 == 1 && p2 == 2 ? 1 : 0);
		
		return func(k - 1, p2, s2, p3, s3, v2, v3);
	}
	
	String gen(int p, int s, int a, int n) {
		String str = "";
		if(p == 0) { str += "B"; }
		else if(p == 2) { str += "C"; }
		for(int i = 0; i < a; i++) {
			str += "AC";
		}
		for(; str.length() < n - 1; ) { str += "B"; }
		if(s == 0) { str += "B"; }
		else if(s == 1) { str += "A"; }
		else if(s == 2) {
			if(str.length() < n - 1 && str.charAt(str.length() - 1) != 'C') {
				str += "C";
			}
		}
		
//		System.err.println(str);
		
		return str;
	}
	
	public void run() throws IOException {
		int k = io.nextInt();
		int x = io.nextInt();
		int n = io.nextInt();
		int m = io.nextInt();

		for(int i = 0; i <= n / 2; i++) {
			// OTHER, A, C
			for(int p1 = 0; p1 < 3; p1++) {
				for(int s1 = 0; s1 < 3; s1++) {
					for(int j = 0; j <= m / 2; j++) {
						for(int p2 = 0; p2 < 3; p2++) {
							for(int s2 = 0; s2 < 3; s2++) {
								if(func(k - 2, p1, s1, p2, s2, i, j) == x) {
									String str1 = gen(p1, s1, i, n);
									String str2 = gen(p2, s2, j, m);
									if(str1.length() == n && str2.length() == m) {
										io.out.println(str1);
										io.out.println(str2);
										return;
									}
								}
							}
						}
					}
				}
			}
		}
		io.out.println("Happy new year!");
	}
	
	static void arrayIntSort(int[][] x, int key) {
		Arrays.sort(x, new IntArrayComparator(key));
	}
	
	static class IntArrayComparator implements Comparator<int[]> {
		final int KEY;
		
		public IntArrayComparator(int key) {
			KEY = key;
		}
		
		@Override
		public int compare(int[] o1, int[] o2) {
			return o1[KEY] - o2[KEY];
		}
	}
	
	void main() throws IOException {
		//		IOFast.setFileIO("rle-size.in", "rle-size.out");
		try {
			run();
		}
		catch (EndOfFileRuntimeException e) { }
		io.out.flush();
	}

	public static void main(String[] args) throws IOException {
		new D().main();
	}
	
	static class EndOfFileRuntimeException extends RuntimeException {
		private static final long serialVersionUID = -8565341110209207657L; }

	static
	public class IOFast {
		private BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
		private PrintWriter out = new PrintWriter(System.out);

		void setFileIO(String ins, String outs) throws IOException {
			in = new BufferedReader(new FileReader(ins));
			out = new PrintWriter(new FileWriter(outs));
		}

		//		private static final int BUFFER_SIZE = 50 * 200000;
		private static int pos, readLen;
		private static final char[] buffer = new char[1024 * 8];
		private static char[] str = new char[500*8*2];
		private static boolean[] isDigit = new boolean[256];
		private static boolean[] isSpace = new boolean[256];
		private static boolean[] isLineSep = new boolean[256];

		static {
			for(int i = 0; i < 10; i++) { isDigit['0' + i] = true; }
			isDigit['-'] = true;
			isSpace[' '] = isSpace['\r'] = isSpace['\n'] = isSpace['\t'] = true;
			isLineSep['\r'] = isLineSep['\n'] = true;
		}

		public int read() throws IOException {
			if(pos >= readLen) {
				pos = 0;
				readLen = in.read(buffer);
				if(readLen <= 0) { throw new EndOfFileRuntimeException(); }
			}
			return buffer[pos++];
		}

		public int nextInt() throws IOException {
			return Integer.parseInt(nextString());
		}

		public long nextLong() throws IOException {
			return Long.parseLong(nextString());
		}

		public char nextChar() throws IOException {
			while(true) {
				final int c = read();
				if(!isSpace[c]) { return (char)c; }
			}
		}
		
		int reads(int len, boolean[] accept) throws IOException {
			try {
				while(true) {
					final int c = read();
					if(accept[c]) { break; }
					
					if(str.length == len) {
						char[] rep = new char[str.length * 3 / 2];
						System.arraycopy(str, 0, rep, 0, str.length);
						str = rep;
					}
					
					str[len++] = (char)c;
				}
			}
			catch(EndOfFileRuntimeException e) { ; }
			
			return len;
		}
		
		int reads(char[] cs, int len, boolean[] accept) throws IOException {
			try {
				while(true) {
					final int c = read();
					if(accept[c]) { break; }
					cs[len++] = (char)c;
				}
			}
			catch(EndOfFileRuntimeException e) { ; }
			
			return len;
		}

		public char[] nextLine() throws IOException {
			int len = 0;
			str[len++] = nextChar();
			len = reads(len, isLineSep);
			
			try {
				if(str[len-1] == '\r') { len--; read(); }
			}
			catch(EndOfFileRuntimeException e) { ; }
			
			return Arrays.copyOf(str, len);
		}

		public String nextString() throws IOException {
			return new String(next());
		}

		public char[] next() throws IOException {
			int len = 0;
			str[len++] = nextChar();
			len = reads(len, isSpace);
			return Arrays.copyOf(str, len);
		}

		public int next(char[] cs) throws IOException {
			int len = 0;
			cs[len++] = nextChar();
			len = reads(cs, len, isSpace);
			return len;
		}

		public double nextDouble() throws IOException {
			return Double.parseDouble(nextString());
		}

		public long[] nextLongArray(final int n) throws IOException {
			final long[] res = new long[n];
			for(int i = 0; i < n; i++) {
				res[i] = nextLong();
			}
			return res;
		}

		public int[] nextIntArray(final int n) throws IOException {
			final int[] res = new int[n];
			for(int i = 0; i < n; i++) {
				res[i] = nextInt();
			}
			return res;
		}

		public int[][] nextIntArray2D(final int n, final int k) throws IOException {
			final int[][] res = new int[n][];
			for(int i = 0; i < n; i++) {
				res[i] = nextIntArray(k);
			}
			return res;
		}

		public int[][] nextIntArray2DWithIndex(final int n, final int k) throws IOException {
			final int[][] res = new int[n][k+1];
			for(int i = 0; i < n; i++) {
				for(int j = 0; j < k; j++) {
					res[i][j] = nextInt();
				}
				res[i][k] = i;
			}
			return res;
		}

		public double[] nextDoubleArray(final int n) throws IOException {
			final double[] res = new double[n];
			for(int i = 0; i < n; i++) {
				res[i] = nextDouble();
			}
			return res;
		}

	}

}