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.Scanner;

public class NewYearStrings {
	/**
	 * Problem parameters
	 */
	
	private static class Pair {
		/***
		 * Integer pair
		 ***/
			public int p1;
			public int p2;
			
			public Pair(int q1, int q2) {
				p1 = q1;
				p2 = q2;
			}
			
		}

	private static int k;
	private static int x;	// required number of "AC" occurences
	private static int n;	// length of x1
	private static int m;	// length of x2
	
	
	private static void initialize() {
	/***
	 * Reads problem parameters
	 ***/
		Scanner scan = new Scanner(System.in);
		k = scan.nextInt();
		x = scan.nextInt();
		n = scan.nextInt();
		m = scan.nextInt();		
	}
	
	private static Pair count1(int n) {
	/***
	 * Returns numbers of appearences of substring x1 in xn and x(n-1)
	 ***/
		// trivial cases
		if(n<=0) return new Pair(0,0);
		if(n==1) return new Pair(1,0);
		if(n==2) return new Pair(0,1);
		
		// recursion
		Pair prev = count1(n-1);
		return new Pair(prev.p1+prev.p2,prev.p1);
	}
	
	private static Pair count2(int n) {
	/***
	 * Returns numbers of appearences of substring x2 in xn and x(n-1)
	 ***/
		// trivial cases
		if(n<=1) return new Pair(0,0);
		if(n==2) return new Pair(1,0);
			
		// recursion
		Pair prev = count2(n-1);
		return new Pair(prev.p1+prev.p2,prev.p1);
	}

	private static Pair count12(int n) {
	/***
	 * Returns numbers of appearences of the substring
	 * x1+x2 in xn and x(n-1)
	 ***/
		// trivial cases
		if(n<=2) return new Pair(0,0);
		if(n==3) return new Pair(1,0);
			
		// recursion
		Pair prev = count12(n-1);
		return new Pair(prev.p1+prev.p2,prev.p1);
	}
	
	private static Pair count21(int n) {
	/***
	 * Returns numbers of appearences of the substring
	 * x2+x1 in xn and x(n-1)
	 ***/
		// trivial cases
		if(n<=3) return new Pair(0,0);
			
		// recursion
		Pair prev = count21(n-1);
		if(n%2==0) return new Pair(prev.p1+prev.p2+1,prev.p1);
		return new Pair(prev.p1+prev.p2,prev.p1);
	}
	

	
	private static Pair count22(int n) {
	/***
	 * Returns numbers of appearences of the substring
	 * x2+x2 in xn and x(n-1)
	 ***/
		// trivial cases
		if(n<=4) return new Pair(0,0);
			
		// recursion
		Pair prev = count22(n-1);
		if(n%2!=0) return new Pair(prev.p1+prev.p2+1,prev.p1);
		return new Pair(prev.p1+prev.p2,prev.p1);
	}
	
	private static String generateX(int size, int q, int c, int a) {
	/***
	 * Generates a string of length 'size' with
	 * 		q occurences of substring "AC",
	 * 		starting with "C" iff c!=0,
	 * 		ending with "A" iff a!=0
	 ***/
		if(c>0) c=1;
		if(a>0) a=1;
		// inappropriate arguments
		
		if(c<0 || a<0 || q<0 || size<0 || size<c+2*q+a) return null;
		
		char[] x = new char[size];
		int pos = 0;
		if(c!=0) {
			x[pos] = 'C';
			pos++;
		}
		for(int i=0;i<q;i++) {
			x[pos] = 'A';
			pos++;
			x[pos] = 'C';
			pos++;
		}
		while(pos<size) {
			x[pos] = 'B';
			pos++;
		}
		if(a!=0) x[size-1] = 'A';
		
		return new String(x);
	}
	
	public static void main(String[] args) {
	/***
	 * Solves problemset/problem/379/D
	 ***/
		
		// Read problem parameters
		initialize();
		
		/*
		// DEBUG
		k = 4;
		x = 2;
		n = 3;
		m = 4;
		*/
		
		// Determine numbers of substring appearences
		int m1	= count1(k).p1; 
		int m2	= count2(k).p1; 
		int m12	= count12(k).p1; 
		int m21	= count21(k).p1; 
		int m22	= count22(k).p1;

		/* Find 
		 * 		q1 = # occurences of "AC" in x1
		 * 		q2 = # occurences of "AC" in x2
		 * 		aj = 1 if xj ends with "A", 0 otherwise
		 * 		cj = 1 if xj begins with "C", 0 otherwise 
		 * such that
		 * 		k = q1*m1 + q2*m2 + a1*c2*m12 + a2*c1*m21 + a2*c2*m22
		 * with constraints
		 * 		n >= c1 + 2*q1 + a1
		 * 		m >= c2 + 2*q2 + a2 
		 */

		int q1=0, q2=0, a1=0, a2=0, c1=0, c2=0;
		
		// upper bound for q2
		int q2Max = Math.min(m/2, x/m2);
		
		boolean found =	false;
		
		q2 = 0;
		while(!found && q2<=q2Max) {
			a2 = 0;
			while(!found && a2<=1 && m>=2*q2+a2) {
				c2 = 0;
				while(!found && c2<=1 && m>=c2+2*q2+a2) {
					a1 = 0;
					while(!found && a1<=1) {
						c1 = 0;
						while(!found && c1<=1) {
							int aux = x - q2*m2 - a1*c2*m12 - a2*c1*m21 - a2*c2*m22;
							if(aux%m1==0) {
								q1 = aux/m1;
								if(n >=c1+2*q1+a1)
									found = true;
							}
							c1++;
						}
						a1++;
					}
					c2++;
				}
				a2++;
			}
			q2++;
		}
		
		if(found) {
			q2--;
			a1--;
			c1--;
			a2--;
			c2--;
			/*
			System.out.println("Solution found!");
			System.out.print("q1 = "+q1+", ");
			System.out.print("q2 = "+q2+", ");
			System.out.print("c1 = "+c1+", ");
			System.out.print("a1 = "+a1+", ");
			System.out.print("c2 = "+c2+", ");
			System.out.print("a2 = "+a2);
			*/
			System.out.println(generateX(n,q1,c1,a1));
			System.out.println(generateX(m,q2,c2,a2));
		}
		else System.out.println("Happy new year!");
	}
}