### Task:

Your job is to take a pair of parametric equations, passed in as strings, and convert them into a single rectangular equation by eliminating the parameter. Both parametric halves will represent linear equations of x as a function of time and y as a function of time respectively. 

The format of the final equation must be `Ax + By = C` or `Ax - By = C` where A and B must be positive and A, B, and C are integers. The final equation also needs to have the lowest possible whole coefficients. Omit coefficients equal to one.

The method is called `para_to_rect` or `EquationsManager.paraToRect` and takes in two strings in the form `x = at +(or -) b` and `y = ct +(or -) d` respectively, where `a` and `c` must be integers, and `b` and `d` must be positive integers. If `a` or `c` is omitted, the coefficient of _t_ is obviously assumed to be 1 (see final case in the example tests). There will NEVER be double signs in the equations inputted (For example: `"x = -12t + -18"` and `"y = -12t - -18"` won't show up.)

### Examples:

```python
para_to_rect("x = 12t + 18", "y = 8t + 7") => "2x - 3y = 15"
```

> __CALCULATION:__  
  x = 12t + 18  
  y = 8t + 7  
  2x = 24t + 36  
  3y = 24t + 21  
  2x - 3y = (24t + 36) - (24t + 21)  
  2x - 3y = 15  

```python
para_to_rect("x = -12t - 18", "y = 8t + 7") => "2x + 3y = -15"
```

> __CALCULATION:__  
  x = -12t - 18  
  y = 8t + 7  
  2x = -24t - 36  
  3y = 24t + 21  
  2x + 3y = (-24t - 36) + (24t + 21)  
  2x + 3y = -15  

```python
para_to_rect("x = -t + 12", "y = 12t - 1") => "12x + y = 143"
```

> __CALCULATION:__  
  x = -t + 12  
  y = 12t - 1  
  12x = -12t + 144  
  y   = 12t  - 1  
  12x + y = 143  

More examples in the sample test cases.

### Notes:

As you can see above, sometimes you'll need to add the two parametric equations after multiplying by the necessary values; sometimes you'll need to subtract them – just get rid of the _t_!

```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 = "import re\n\nEQUATION_REGEXP = re.compile(r'^[xy]=(-?\\d*)t([+-]\\d+)$')\n\n\ndef parse_coefficient(raw_coef):\n    if not raw_coef:\n        return 1\n    elif raw_coef == '-':\n        return -1\n    return int(raw_coef)\n\n\ndef parse(equation):\n    equation = equation.replace(' ', '')\n    coefficients = EQUATION_REGEXP.match(equation).groups()\n    return list(map(parse_coefficient, coefficients))\n\n\ndef gcd(a, b):\n    return gcd(b, a % b) if b else a\n\n\ndef lcm(a, b):\n    return abs(a * b) / gcd(a, b)\n\n\ndef compile_result(mult_a, mult_b, coefs_a, coefs_b):\n    multiplier = -1 if mult_a < 0 else 1\n\n    A = mult_a * multiplier\n    A = A if A != 1 else ''   \n    \n    B = abs(mult_b) if abs(mult_b) != 1 else ''\n    B_sign = '-' if multiplier * mult_b > 0 else '+'\n    \n    C = multiplier * (mult_a * coefs_a[1] - mult_b * coefs_b[1])\n\n    return f'{A}x {B_sign} {B}y = {C}'\n\n\ndef para_to_rect(equation_a, equation_b):\n    coefs_a = parse(equation_a)\n    coefs_b = parse(equation_b)\n    parameter_lcm = int(lcm(coefs_a[0], coefs_b[0]))\n    mult_a = int(parameter_lcm / coefs_a[0])\n    mult_b = int(parameter_lcm / coefs_b[0])\n    return compile_result(mult_a, mult_b, coefs_a, coefs_b)\n    \n"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'para_to_rect'
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: 6999