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:
//Author: net12k44
import java.io.InputStreamReader;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.OutputStream;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.StringTokenizer;
import java.util.Calendar;
public
class Main{//}
	
static PrintWriter out;
static long x; static int m,  n , k;
static long f[][][];
static long s[] = new long [2];
static char vt[] = new char[3];

static String check(int n , int dau , int cuoi , long sl) {
	if (n == 1 && dau != cuoi) return null;
	char a[] = new char[n];
	for(int i = 0; i < n; ++i) a[i] = 'B';
	a[0] = vt[ dau ]; 
	int i = 0; if (a[0] != 'A') ++i;
	int t = 0;
	while (t++ < sl && i+1 < n) {
		a[i] = 'A'; a[i+1] = 'C';
		i+=2;
	}
	
	t = 0;
	a[n-1] = vt[cuoi];
	for(i = 0; i < n-1; ++i) if (a[i] == 'A' && a[i+1] == 'C') t++;
	if (t != sl) return null;
	return new String(a);
	

}

static boolean ktra(int d , int c , int Dau , int Cuoi, long x) {
	vt[0] = 'A'; vt[1] = 'C'; vt[2] = 'B';
	int dau[]  = new int [2]; dau [0] = d; dau [1] = Dau;
	int cuoi[] = new int [2]; cuoi[0] = c; cuoi[1] = Cuoi;
	for(int i = 0; i < 2; ++i)
	for(int j = 0; j < 2; ++j)
	 if ( cuoi[i] == 0 && dau[j] == 1 ) x -= f[k][i][j];
	
	if (x < 0) return false;
	
	for(long i0 = 0; i0 <= n/2; ++i0) {
		long i1 = x - s[0] * i0;
		if (i1 < 0) break;
		if (i1 % s[1] != 0) continue;
		i1 = i1 / s[1];
		String s1 = check(n , d , c , i0);
		String s2 = check(m , Dau , Cuoi , i1);
		if (s1 == null || s2 == null) continue;
		out.println(s1);
		out.println(s2);
		return true;
	}
	
	
	return false;
}

static void solve() throws IOException{
	k = in.nextInt(); x = in.nextInt(); n = in.nextInt(); m = in.nextInt();
	f = new long[k+1][2][2];
	int dau[] = new int [k+1] , cuoi[] = new int[k+1];
	
	dau[1] = cuoi[1] = 0;
	dau[2] = cuoi[2] = 1;
	
	for(int i = 3; i <= k; ++i) {
		for(int j = 0; j < 2; ++j)
		for(int t = 0; t < 2; ++t)
			f[i][j][t] = f[i-1][j][t] + f[i-2][j][t] + ( ( cuoi[i-2] == j && dau[i-1] == t ) ? 1 : 0 );
		
		dau[i] = dau[i-2];
		cuoi[i] = cuoi[i-1];		
	}
		
	s[0] = f[k][0][0] * 2 + f[k][0][1] + f[k][1][0];
	s[1] = f[k][1][1] * 2 + f[k][0][1] + f[k][1][0];
	s[ dau[k]  ] ++;
	s[ cuoi[k] ] ++;
	//out.println(s[1]);
	s[0] /= 2; s[1] /= 2;
		
	for(int dau1 = 0; dau1 < 3; ++dau1)
	for(int cuoi1 = 0; cuoi1 < 3; ++cuoi1)
	for(int dau2 = 0; dau2 < 3; ++dau2)
	for(int cuoi2 = 0; cuoi2 < 3; ++cuoi2)
	  if ( ktra( dau1 , cuoi1 , dau2 , cuoi2 ,x  ) ) return;
	  
	out.println("Happy new year!");
	/**/
	
	
}
	
public static void main (String[] args) throws java.lang.Exception {
	//String home = System.getProperty("NAM");
	//long startTime = System.currentTimeMillis();
	in.init();		
	out = new PrintWriter(System.out);
	solve();
	/*if ( System.getProperty("NAM") != null) {		
		long endTime   = System.currentTimeMillis();
		out.println( String.format( "%.2f" , (double)(endTime-startTime) / 1000 ) );
	}*/
	out.close();
}
	
static class in {
	static BufferedReader reader;
	static StringTokenizer tokenizer;
		
	static void init() {
		reader = new BufferedReader(
					 new InputStreamReader(System.in) );
		tokenizer = new StringTokenizer("");
	}
		
	static String next() throws IOException {
		while ( ! tokenizer.hasMoreTokens() ) {			
			tokenizer = new StringTokenizer(
				   reader.readLine() );
		}
		return tokenizer.nextToken();
	}

	static int nextInt() throws IOException {
		return Integer.parseInt( next() );
	}
		
	static double nextDouble() throws IOException {
		return Double.parseDouble( next() );
	}
}
//////////////////////////////////////////////////
}//