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.InputStreamReader;
import java.io.IOException;
import java.util.InputMismatchException;
import java.io.PrintStream;
import java.io.BufferedReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.Reader;
import java.io.Writer;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 * @author Nipuna Samarasekara
 */
public class Main {
	public static void main(String[] args) {
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		FastScanner in = new FastScanner(inputStream);
		FastPrinter out = new FastPrinter(outputStream);
		TaskD solver = new TaskD();
		solver.solve(1, in, out);
		out.close();
	}
}

class TaskD {
    /////////////////////////////////////////////////////////////

    public void solve(int testNumber, FastScanner in, FastPrinter out) {
    int k=in.nextInt(),x=in.nextInt(),n=in.nextInt(),m=in.nextInt();
    long[] s1 = new long [k+2];  // k ones
    long[] s2 = new long [k+2] ; // k ones
    long[] se = new long [k+2] ; // k ones
 long[] ss = new long [k+2] ; // k ones
   int[] m1= new int[n];
        int[] m2= new int[m];
        for (int i = 0; i <n; i++) {
            m1[i]=2;
        }
        for (int i = 0; i < m; i++) {
            m2[i]=2;
        }

        long[] s12 = new long [k+2];  // k ones
        long[] s21 = new long [k+2] ; // k ones
        long[] s11 = new long [k+2];  // k ones
        long[] s22 = new long [k+2] ; // k ones
        s2[2]=1;se[2]=2;ss[2]=2;
        s1[1]=1;se[1]=1;ss[1]=1;
      int found=0;
        int p1=0,p2=0;
        for (int i = 3; i <= k; i++) {
          s1[i]=s1[i-1]+s1[i-2];
          s2[i]=s2[i-1]+s2[i-2];
           se[i]= se[i-1]; ss[i]=ss[i-2];
            s11[i]+=s11[i-1]+s11[i-2];
            s12[i]+=s12[i-1]+s12[i-2];
            s21[i]+=s21[i-1]+s21[i-2];
            s22[i]+=s22[i-1]+s22[i-2];
        if(se[i-2]==1&&ss[i-1]==1)  s11[i]++;
        if(se[i-2]==1&&ss[i-1]==2)  s12[i]++;
        if(se[i-2]==2&&ss[i-1]==1)  s21[i]++;
        if(se[i-2]==2&&ss[i-1]==2)  s22[i]++;  }
//        deb(s11);
//        deb(s21);
            for (int s1s = 0; s1s < 3; s1s++) {
                for (int s1e = 0; s1e < 3; s1e++) {
                    for (int s2s = 0; s2s < 3; s2s++) {
                        for (int s2e = 0; s2e < 3; s2e++) {
                            long bonus=0;
                           if(n==1&&s1s!=s1e)continue;
                           if(m==1&&s2s!=s2e)continue;

                            if(s1e==0&&s2s==1)bonus+=s12[k];
                            if(s1e==0&&s1s==1)bonus+=s11[k];
                            if(s2e==0&&s2s==1)bonus+=s22[k];
                            if(s2e==0&&s1s==1)bonus+=s21[k];
                         long want= x-bonus;
                            if(want<0)continue;
                        long max1,max2;
                         if(s1s==0&&s1e==1){
                             max1=n/2;}
                         else if(s1s!=0&&s1e==1){
                             max1=(n-1)/2;}
                         else  if(s1s==0&&s1e!=1){
                             max1=(n-1)/2;}
                         else max1=(n-2)/2;

                            if(s2s==0&&s2e==1){
                                max2=m/2;}
                            else if(s2s!=0&&s2e==1){
                                max2=(m-1)/2;}
                            else  if(s2s==0&&s2e!=1){
                                max2=(m-1)/2;}
                            else max2=(m-2)/2;
//                           if(s1s==0&&s1e==2&&s2s==1&&s2e==0){
//                               System.out.println(bonus+ " saf "+want+" "+x);
//                           }
                            for (int j = 0; j <= max1; j++) {
                                 if(n==2&&s1s==0&&s1e==1&&j==0)continue;
                                for (int l = 0; l <= max2; l++) {
                                    if(m==2&&s2s==0&&s2e==1&&l==0)continue;
                                    long sum= (long)j*s1[k]+(long)l*s2[k];
                                  if(sum==want){
                                   found=1;
                                      m1[0]=s1s;
                                      m2[0] =s2s;
                                      m1[n-1]=s1e;
                                      m2[m-1]=s2e;
                                      p1=j;p2=l;
                                      break;
                                  }
                                   if(sum>want)break;
                                }
                                if(found==1)break;
                            }
                            if(found==1)break;

                        }
                        if(found==1)break;
                    }
                    if(found==1)break;
                }
                if(found==1)break;
            }


        if(found==0)
            out.println("Happy new year!");
        else {
            int st=1;
           if(m1[0]==0&&p1>0){
               p1--;
              m1[1]=1; st=2;
           }
            while(p1>0){
                p1--;
                m1[st]=0;st++;
                m1[st]=1;st++;

            }
             st=1;
           if(m2[0]==0&&p2>0){
               p2--;
              m2[1]=1; st=2;
           }
            while(p2>0){
                p2--;
                m2[st]=0;st++;
                m2[st]=1;st++;

            }
           StringBuilder sb= new StringBuilder();
            for (int i = 0; i < n; i++) {
                if(m1[i]==0)sb.append('A');
                if(m1[i]==1)sb.append('C');
                if(m1[i]==2)sb.append('B');
            }
            out.println(sb.toString());
            sb= new StringBuilder();
            for (int i = 0; i < m; i++) {
                if(m2[i]==0)sb.append('A');
                if(m2[i]==1)sb.append('C');
                if(m2[i]==2)sb.append('B');
            }
            out.println(sb.toString());
        }
    }
}

class FastScanner extends BufferedReader {

    public FastScanner(InputStream is) {
        super(new InputStreamReader(is));
    }

    public int read() {
        try {
            int ret = super.read();
//            if (isEOF && ret < 0) {
//                throw new InputMismatchException();
//            }
//            isEOF = ret == -1;
            return ret;
        } catch (IOException e) {
            throw new InputMismatchException();
        }
    }

    static boolean isWhiteSpace(int c) {
        return c >= 0 && c <= 32;
    }

    public int nextInt() {
        int c = read();
        while (isWhiteSpace(c)) {
            c = read();
        }
        int sgn = 1;
        if (c == '-') {
            sgn = -1;
            c = read();
        }
        int ret = 0;
        while (c >= 0 && !isWhiteSpace(c)) {
            if (c < '0' || c > '9') {
                throw new NumberFormatException("digit expected " + (char) c
                        + " found");
            }
            ret = ret * 10 + c - '0';
            c = read();
        }
        return ret * sgn;
    }

    public String readLine() {
        try {
            return super.readLine();
        } catch (IOException e) {
            return null;
        }
    }

    }

class FastPrinter extends PrintWriter {

    public FastPrinter(OutputStream out) {
        super(out);
    }

    public FastPrinter(Writer out) {
        super(out);
    }


}