Good Bye 2013 D

D. New Year Letter

time limit per test 1 second

memory limit per test 256 megabytes

 

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 s_k, using a recurrent equation s_n = s_n - 2 + s_n - 1, operation '+' means a concatenation (that is, the sequential record) of strings in the given order. Then Vasya writes down string s_k 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 s_k 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.

Sample test(s)

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!

#pragma comment(linker,"/STACK:102400000,102400000")
#include <cstdio>
#include <vector>
#include <cmath>
#include <stack>
#include <queue>
#include <cstring>
#include <iostream>
#include <algorithm>
using namespace std;
#define INF 0x7fffffff
#define mod 1000000007
#define ll long long
#define maxn 206
#define pi acos(-1.0)                                             
#define FF(i,n) for(int i=0;i<n;i++)
ll n, m, z, t, flag, k, x,y; 
ll f[maxn];
int main(){
    cin >> k >> x >> n >> m;
    for (int i = 0; i <= n / 2; i++)
    for (int j = 0; j <= m / 2; j++)
    for (int a = 0; a < 2; a++)
    for (int b = 0; b < 2; b++)
    for (int c = 0; c < 2; c++)
    for (int d = 0; d < 2; d++){
        if (i * 2 + a + b > n||j * 2 + c + d > m)continue;
        f[1] = i; f[2] = j; t = 0;
        if (b && c)t++;
        for (z = 3; z <= k; z++){
            f[z] = f[z - 1] + f[z - 2];
            if (t)f[z]++, t--;
            if (z>3&&d&&a&&z % 2 == 0)f[z]++;
            if (z>3&&d&&c&&z % 2 == 1)f[z]++;
        }
        if (f[k] == x){
            if (a)printf("C");
            for (int z = 0; z < i; z++)printf("AC");
            for (int z = 0; z < n-i*2-a-b; z++)printf("M");
            if (b)printf("A"); puts("");
            if (c)printf("C"),z++;
            for (int z = 0; z < j; z++)printf("AC");
            for (int z = 0; z < m-j*2-c-d; z++)printf("M");
            if (d)printf("A"); puts("");
            return 0;
        }
    }
    printf("Happy new year!\n");
    return 0;
}