# Introduction 

Digital Cypher assigns a unique number to each letter of the alphabet:

```
 a  b  c  d  e  f  g  h  i  j  k  l  m  n  o  p  q  r  s  t  u  v  w  x  y  z
 1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
```

In the encrypted word we write the corresponding numbers instead of the letters. For example, the word `scout` becomes:

```
 s  c  o  u  t
19  3 15 21 20
```
Then we add to each number a digit from the key (repeated if necessary). For example if the key is `1939`:

```
   s  c  o  u  t
  19  3 15 21 20
 + 1  9  3  9  1
 ---------------
  20 12 18 30 21
  
   m  a  s  t  e  r  p  i  e  c  e
  13  1 19 20  5 18 16  9  5  3  5
+  1  9  3  9  1  9  3  9  1  9  3
  --------------------------------
  14 10 22 29  6 27 19 18  6  12 8
```

# Task

Write a function that accepts a `message` string  and an array of integers `code`. As the result, return the `key` that was used to encrypt the `message`. The `key` has to be shortest of all possible keys that can be used to code the `message`: i.e. when the possible keys are `12` , `1212`, `121212`, your solution should return `12`.

#### Input / Output:

* The `message` is a string containing only lowercase letters.
* The `code` is an array of positive integers.
* The `key` output is a positive integer.

# Examples

```python
find_the_key("scout", [20, 12, 18, 30, 21]) # -->  1939
find_the_key("masterpiece", [14, 10, 22, 29, 6, 27, 19, 18, 6, 12, 8]) # -->  1939
find_the_key("nomoretears", [15, 17, 14, 17, 19, 7, 21, 7, 2, 20, 20]) # -->  12
```

# Digital cypher series
- [Digital cypher vol 1](https://www.codewars.com/kata/592e830e043b99888600002d)
- [Digital cypher vol 2](https://www.codewars.com/kata/592edfda5be407b9640000b2)
- [Digital cypher vol 3 - missing key](https://www.codewars.com/kata/5930d8a4b8c2d9e11500002a)

```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

def _disabled_input(*args, **kwargs):
    raise RuntimeError("input() is disabled in callable mode")
builtins.input = _disabled_input

ns = {"__name__": "__judge__"}  # prevent if __name__ == "__main__" blocks
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = "from string import ascii_lowercase as al\n\ndef find_the_key(message, code):\n    msg_key = ''.join([str(a - d) for (a, d) in zip(code, [al.index(c) + 1 for c in message])])\n    key, len_msg = '', len(msg_key)\n    for i, n in enumerate(msg_key, 1):\n        key += n\n        d, m = divmod(len_msg, i)\n        test_key = key * (d + (m > 0))  # round up integer without math.ceil\n        if test_key[:len_msg] == msg_key:\n            return int(key)"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'find_the_key'
if _fn_name:
    if "Solution" in ns:
        try:
            _obj = ns["Solution"]()
            if hasattr(_obj, _fn_name):
                _target = getattr(_obj, _fn_name)
        except Exception:
            _target = None
    if _target is None and _fn_name in ns and callable(ns[_fn_name]):
        _target = ns[_fn_name]
# Fallback: if there's exactly one user-defined function, use it
if _target is None:
    _cands = [v for k, v in ns.items() if callable(v) and getattr(v, "__module__", "") in ("__judge__", "__main__")]
    _user_funcs = [c for c in _cands if getattr(c, "__name__", "").startswith("_") is False]
    if len(_user_funcs) == 1:
        _target = _user_funcs[0]
if _target is None:
    raise RuntimeError(f"Could not resolve callable '{_fn_name}'")

_raw = sys.stdin.read().strip()
if _raw:
    _parsed = json.loads(_raw)
    if isinstance(_parsed, dict):
        _kwargs = _parsed.get("kwargs", {})
        _args = _parsed.get("args", [])
    else:
        _args, _kwargs = _parsed, {}
else:
    _args, _kwargs = [], {}
if not isinstance(_args, (list, tuple)):
    _args = [_args]
_res = _target(*_args, **_kwargs)
try:
    sys.stdout.write(repr(_res) + "\n")
except Exception:
    pass

```

Measured memory_bytes: 6330