John was learning mathematics and was very bored. Jane his best friend gave him a problem to solve. 
The description of the problem was as follows:- 
You are given a decimal number $N$(1<=$N$<=$10^9$) and three integers $A$, $B$, $C$. 
Steps to perform:
1) You have to create a $LIST$. 
2) You have to initialize the $LIST$ by adding N to the $LIST$ as its first element. 
3) Divide$N$ by $A$ and if the first digit of the fractional part is Non-Zero then add this digit to the  $LIST$ otherwise add the first digit of the integral part(Leftmost digit).
(The integer part or integral part of a decimal is the integer written to the left of the decimal separator.  The part from the decimal separator i.e to the right is the fractional part. )
4) Update $N$  by Last element of the $LIST$. 
N = Last element of $LIST$
5) You have to perform the same process from step 3 on $N$ for $B$ and $C$ respectively 
6) Repeat from step 3 
You have to answer$Q$(1 <= $Q$<= 100 ) queries
For each query you are given an integer $i$ (0 <= $i$ <= $10^9$ ). You have to print the element present at the ith position of the $LIST$. 
Help John solve this problem.

-----Input:-----
- The First Line of input contains a single integer $T$ denoting the number of test cases. The description of $T$ test cases follows.
- The First Line of each test case contains the  integer $N$.
- The second line of each test case contains three integers $A$, $B$, and $C$ separated by a space
- The third line of each test case contains an integer $Q$.
- Then the next $Q$ line follows.  
- An integer $i$ (0 <= $i$ <= 10^9 )

-----Output:-----
You have to answer the $Q$ queries in the next $Q$ lines. 

-----Constraints-----
- $1 \leq T \leq 10$
- $1 \leq N \leq 10^9$
- $2 \leq A \leq 10$
- $2 \leq B \leq 10$
- $2 \leq C \leq 10$
- $2 \leq Q \leq 100$
- $0 \leq i \leq 10^9$

-----Sample Input:-----
1
56
3 5 7
4
0
1
2
3

-----Sample Output:-----
56
6
2
2

-----EXPLANATION:-----
This list is :
$N$ = 56 and $A$ = 3, $B$ = 5, $C$ = 7. 
Initially $LIST$ = $[ 56 ]$
$N$$/$$A$ =  56/3 = 18.666666666666668 
Add 6 to the $LIST$ 
$LIST$ = $[ 56, 6 ]$
$N$ = 6 
$N$$/$$B$ = 6/5 = 1.2 
Add 2 to the$LIST$ 
$LIST$ = $[ 56, 6, 2 ]$
N = 2 
$N$$/$$C$ = 2/7 =0. 2857142857142857
Add 2 to the $LIST$.  
$LIST$ = $[ 56, 6, 2, 2 ]$
$N$  = 2
We have to keep repeating this process. If any of the numbers got by $N$ dividing by either $A$, $B$, $C$ have 0 after the decimal point then we have to take the first digit of the number. 
for example: if we got 12.005 then here we take 1 and add it to the list and then assign N = 1 
Now the queries ask for the elements at index 0, 1, 2, 3 of the $LIST$ which is 56,6, 2, 2

```python

USER_FILENAME = "<user_code>"
import sys, json, builtins
import math, heapq, bisect, itertools, functools, collections, statistics, fractions, decimal, operator, array, random, re, string, os, pathlib
try:
    import resource as _res
except Exception:
    _res = None
from collections import Counter, defaultdict, deque, OrderedDict
from functools import lru_cache, reduce
from itertools import accumulate, permutations, combinations, product
from math import gcd, ceil, floor, sqrt
from decimal import Decimal
try:
    from typing import *
except Exception:
    pass
try:
    sys.setrecursionlimit(1_000_000)
except Exception:
    pass
try:
    import site as _site
    try:
        _sys_sites = _site.getsitepackages() if hasattr(_site, "getsitepackages") else []
        for _p in _sys_sites:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
    try:
        _usp = _site.getusersitepackages()
        if isinstance(_usp, str):
            _usp = [_usp]
        for _p in _usp:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
except Exception:
    pass

ns = {"__name__": "__main__"}
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = 'T = int(input())\nfor t in range(T):\n\n\tn = int(input())\n\ty = list(map(int, input().split()))\n\tx = [n]\n\n\ti = 0\n\tprev = x[0]\n\n\tvisited = [{}, {}, {}]\n\n\telement = 1\n\tcycle_length = -1\n\tcycle_start = -1\n\twhile True:\n\t\ta = y[i]\t\n\t\t#print(i)\n\t\tmod = prev % a\n\t\tdiv = mod / a\n\t\tdigit = int(str(div)[2])\n\t\tif digit == 0:\n\t\t\tdigit = int(str(prev // a)[0])\n\n\t\tif digit in visited[i]:\n\t\t\tcycle_length = element - visited[i][digit]\n\t\t\tcycle_start = visited[i][digit]\n\t\t\tbreak\n\t\telse:\n\t\t\tvisited[i][digit] = element\n\n\t\tx.append(digit)\n\t\tprev = int(digit)\n\n\t\telement += 1\n\t\ti = (i + 1) % 3\n\n\tQ = int(input())\n\tfor q in range(Q):\n\t\tidx = int(input())\n\t\tif idx < len(x):\n\t\t\tprint(x[idx])\n\n\t\telse:\n\t\t\tidx -= cycle_start\n\t\t\tidx = idx % cycle_length\n\t\t\tprint(x[cycle_start + idx])\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13577