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 CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
const long double PI = acosl(-1.0);
const double EPS = 1e-12;
void showBit(int no, int N) {
  for (int i = N - 1; i >= 0; i--)
    if ((no >> i) & 1)
      printf("1");
    else
      printf("0");
  printf("\n");
}
int binToDec(string s) {
  int ln = s.length();
  int sum = 0;
  for (int i = ln - 1, k = 0; i >= 0; i--, k++)
    sum = sum + (s[i] - '0') * (1 << k);
  return sum;
}
void combination(long long com[][1005]) {
  com[0][0] = 1;
  int sz = 1000;
  for (int i = 1; i <= sz; i++) {
    com[i][0] = 1;
    for (int j = 1; j <= i; j++) {
      com[i][j] = com[i - 1][j] + com[i - 1][j - 1];
      com[i][j] = com[i][j] % 1000000007;
    }
  }
}
int find_par(int cn) {}
int gcd(int u, int v) {
  if (v == 0) return u;
  return gcd(v, u % v);
}
void insert_ind(int cs, int ci, int s, int e) {
  if (s == e) {
    return;
  }
  int mid = (s + e) / 2;
  if (ci <= mid)
    insert_ind(2 * cs, ci, s, mid);
  else
    insert_ind(2 * cs + 1, ci, mid + 1, e);
}
void update_ind(int cs, int ci, int s, int e, int val) {
  if (s == e) {
    return;
  }
  int mid = (s + e) / 2;
  if (ci <= mid)
    update_ind(2 * cs, ci, s, mid, val);
  else
    update_ind(2 * cs + 1, ci, mid + 1, e, val);
}
void update_seg(int cs, int ds, int de, int s, int e, int val) {
  if (ds == s && de == e) {
    return;
  }
  int mid = (s + e) / 2;
  if (ds <= mid) update_seg(2 * cs, ds, min(mid, de), s, mid, val);
  if (de > mid) update_seg(2 * cs + 1, max(mid + 1, ds), de, mid + 1, e, val);
}
void pattern_match(char pat[], const int len, int pi[]) {
  pi[1] = 0;
  for (int i = 2; i <= len; i++) {
    int st = i - 1;
    while (st >= 0 && pat[pi[st] + 1] != pat[i]) st = pi[st];
    if (st == 0)
      pi[i] = 0;
    else
      pi[i] = pi[st] + 1;
  }
}
void pattern_match(char pat[], int pi[], char tar[], const int len1, int gi[]) {
  if (pat[0] == tar[0]) gi[0] = 1;
  for (int i = 1; i < len1; i++) {
    int st = gi[i - 1];
    while (pat[st] != tar[i]) {
      if (st == 0) {
        st = -1;
        break;
      }
      st = pi[st - 1];
    }
    if (st == -1)
      gi[i] = 0;
    else
      gi[i] = st + 1;
  }
}
struct myArray {
  int mat[10][10];
};
myArray matrix_mul(myArray mat1, myArray mat2, const int sz) {
  int tmp[sz][sz];
  memset((tmp), 0, sizeof((tmp)));
  for (int r = 0; r < sz; r++)
    for (int c = 0; c < sz; c++)
      for (int cr = 0; cr < sz; cr++)
        tmp[r][c] += mat1.mat[r][cr] * mat2.mat[c][cr];
  myArray res;
  for (int r = 0; r < sz; r++)
    for (int c = 0; c < sz; c++) res.mat[r][c] = tmp[r][c];
  return res;
}
myArray unit_matrix(const int sz) {
  myArray ma;
  memset((ma.mat), 0, sizeof((ma.mat)));
  for (int i = 0; i < sz; i++) ma.mat[i][i] = 1;
  return ma;
}
myArray matrix_expo(int p, myArray mat, const int sz) {
  if (p == 0) {
    return unit_matrix(sz);
  }
  if (p & 1) return matrix_mul(mat, matrix_expo(p - 1, mat, sz), sz);
  myArray tmp = matrix_expo(p >> 1, mat, sz);
  return matrix_mul(tmp, tmp, sz);
}
int X[] = {0, 0, 1, -1};
int Y[] = {1, -1, 0, 0};
int k, x, n, m;
char s1[105], s2[105];
void makeString(int rp, int fl, int fr, char s[], int ln) {
  bool print = false;
  s[0] = '\0';
  int r = ln - (rp * 2);
  if (rp == 0) {
    if (ln == 2 && fl == 0 && fr == 2) return;
    if (ln == 1 && fl != fr) return;
    s[0] = 'A' + fl;
    for (int i = 1; i < ln - 1; i++) s[i] = 'B';
    s[ln - 1] = 'A' + fr;
    s[ln] = '\0';
  } else {
    if (r == 0) {
      if (!(fl == 0 && fr == 2)) return;
      for (int i = 0; i < ln; i++) s[i] = (i & 1) ? 'C' : 'A';
      s[ln] = '\0';
    } else if (r == 1) {
      if (fl == 0) {
        for (int i = 0; i < ln - 1; i++) s[i] = (i & 1) ? 'C' : 'A';
        s[ln - 1] = 'A' + fr;
        s[ln] = '\0';
      } else if (fr == 2) {
        s[0] = 'A' + fl;
        for (int i = 1; i < ln; i++) s[i] = (i & 1) ? 'A' : 'C';
        s[ln] = '\0';
      }
    } else {
      s[0] = 'A' + fl;
      for (int i = 1; i <= rp; i++) {
        s[2 * i - 1] = 'A';
        s[2 * i] = 'C';
      }
      for (int i = 1 + 2 * rp; i < ln; i++) s[i] = 'A' + fr;
      s[ln] = '\0';
    }
  }
}
int cal(int rp1, int fl, int fr, int rp2, int sl, int sr) {
  int crp = 0, t = 0;
  bool print = false;
  for (int i = 3; i <= k; i++) {
    crp = rp1 + rp2;
    if (fr == 0 && sl == 2) crp++;
    t = crp;
    if (t > x) return -1;
    int tfl = fl;
    rp1 = rp2;
    fl = sl;
    fr = sr;
    rp2 = crp;
    sl = tfl;
    sr = sr;
  }
  return t;
}
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 fl = 0; fl < 3; fl++)
        for (int fr = 0; fr < 3; fr++)
          for (int sl = 0; sl < 3; sl++)
            for (int sr = 0; sr < 3; sr++) {
              makeString(i, fl, fr, s1, n);
              makeString(j, sl, sr, s2, m);
              if (s1[0] == '\0' || s2[0] == '\0') continue;
              int res = cal(i, fl, fr, j, sl, sr);
              if (res == x) {
                puts(s1);
                puts(s2);
                return 0;
              }
            }
  printf("Happy new year!");
  return 0;
}