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 PYTHON):

Solution:
import os,sys

###newYearLetter 397D, http://codeforces.com/problemset/problem/379/D
###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.
def verify(k, x, c1, a1, cntAC1, c2, a2, cntAC2):
    ##sk could have exactly x 'ac'
    count = 0
    if k <= 0:
        return 0==x
    if 1 == k:
        return cntAC1==x
    if 2 == k:
        return cntAC2==x

    while k > 2:
        count = cntAC1 + cntAC2 + a1*c2##current number of ac in sk
        if count > x:
            return False

        cntAC1 = cntAC2
        cntAC2 = count

        tmp = c1
        c1 = c2
        c2 = tmp
        a1 = a2
        k -= 1
    return count==x
        
def constructStr(c, a, cntAC, num):
    numOfX = num - c - a - 2*cntAC
    res = ""
    if 1 == c:
        res += 'C'
    for i in range(cntAC):
        res += 'AC'
    for i in range(numOfX):
        res += 'X'
    if 1 == a:
        res += 'A'
    return res
######
##consider s1 = [c1](ac)(x)[a1], s2 = [c2](ac)(x)[a2]
def run():
    k, x, n, m = map(int, raw_input().split())
    for c1 in range(2):###number of c in the begin of s1
        for a1 in range(2):###number of a in the end of s1
            for cntAC1 in range((n-c1-a1)/2+1):###number of AC in s1
                for c2 in range(2):###number of c in the begin of s2
                    for a2 in range(2):###number of a in the end of s2
                        for cntAC2 in range((m-c2-a2)/2+1):
                            if True == verify(k, x, c1, a1, cntAC1, c2, a2, cntAC2):
                                s1 = constructStr(c1, a1, cntAC1, n)
                                s2 = constructStr(c2, a2, cntAC2, m)
                                print s1
                                print s2
                                return
    print 'Happy new year!'
########################################################################################
run()