## Task

Let's say we have a positive integer, `$n$`. You have to find the smallest possible positive integer that when multiplied by `$n$`, becomes a perfect power of integer `$k$`. A perfect power of `$k$` is any positive integer that can be represented as `$a^k$`. For example if `$k = 2$`, then `$36$` is a perfect power of `$k$`, but `$27$` isn't.

## Examples

```python
n, k = 100, 3  return  10, #because 10*100 becomes 1000, and 1000 = 10**3
n, k = 36, 2   return   1, #because 36 is already a perfect square 6**2
n, k = 72, 4   return  18, #because 18*72 = 1296 = 6**4
```

**Notes:** 
+ `$k, n \in \mathbb{N} $` and `$ 1 \lt n \lt 10^6,\text{ } 1 \lt k \lt 10 $`
+ However, the output may be way larger than `$10^6$`.

If you have trouble seeing the numbers, refresh your page ;-) Please rate this kata. All translations are welcome.

ABOVE: [If you see this:](https://imgur.com/TKY59S4), refresh your page.

```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 = 'def mul_power(n, k):\n    z = []\n    f = []\n    g = []\n    for i in range(1,n+1):\n        if n % i == 0:\n            z.append(i)\n            print(z)\n   \n    for c in z:\n        f.append(c**k)\n        print(f)\n   \n    for j in f:\n        g.append(j//n)\n        print(g)\n    for ele in g:\n        if ele*n in f:\n            return ele\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'mul_power'
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: 8708