A **pandigital number** is one that has its digits from ```1``` to ```9``` occuring only once (they do not have the digit 0).

The number ```169```, is the first pandigital square, higher than ```100```, having its square root, ```13```, pandigital too.

The number ```1728``` is the first pandigital cubic, higher than ```1000```, having its cubic root, ```12```, pandigital too.

Make the function ```pow_root_pandigit()```, that receives three arguments:

- a minimum number, ```val```

- the exponent of the n-perfect powers to search, ```n```

- ```k```, maximum amount of terms that we want in the output

The function should output a 2D-array with an amount of k pairs of numbers(or an array of an only pair if we have this case). Each pair has a nth-perfect power pandigital higher than val with its respective nth-root that is pandigital, too.

The function should work in this way:
```python
pow_root_pandigit(val, n, k) = [[root1, pow1], [root2, pow2], ...., [rootk, powk]]
"""
root1 < root2 <.....< rootk
val < pow1 < pow2 < ....< powk
root1 ^ n = pow1 // root2 ^ n = pow2 //........// rootk ^ n = powk
all pairs rooti, powi are pandigitals
"""
```
Let's see some examples:
```python
pow_root_pandigit(388, 2, 3)== [[23, 529], [24, 576], [25, 625]] # 3 pairs (k = 3)
```
For a different power:
```python
pow_root_pandigit(1750, 3, 5) == [[13, 2197], [17, 4913], [18, 5832], [19, 6859], [21, 9261]] # 5 pairs (k = 5)
```

The output in not inclusive for val.
```python
pow_root_pandigit(1728, 3, 4) == [[13, 2197], [17, 4913], [18, 5832], [19, 6859]]
# ∛1728 = 12
```

The result may have less terms than the required:
```python
pow_root_pandigit(600000000, 2, 5) == [25941, 672935481] # If the result has an only one pair, the output is an array
```
Furthermore, if the minimum value, ```val``` is high enough, the result may be an empty list:
```python
pow_root_pandigit(900000000, 2, 5) == []
```

You may suposse that the input ```val```, ```n``` will be always:  ```val > 10``` and ```n > 2```.

Enjoy it!!

```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 itertools import permutations as p\n\nn_str = '123456789'\nformt = lambda n: sorted(list(map(''.join, list(filter(set, p(n_str, n))))))\ndb = formt(1) + formt(2) + formt(3) + formt(4) + formt(5)\nhs = {1:0, 2:9, 3:81, 4:585, 5:3609}\n\ndef next_pandigital(lp):\n    if lp in db:\n        return db[db.index(lp):]\n    while 1:\n        lp = str(int(lp) + 1)\n        if lp in db[hs[len(lp)]:]:\n            break\n    return db[db.index(lp):]\n\ndef is_pandigital(lp):\n    return len(set(lp)) == len(lp) and '0' not in lp\n\ndef pow_root_pandigit(val, n, k):\n    l = []\n    low = int(val ** (1 / n) + 0.0001) + 1\n    for p in next_pandigital(str(low)):\n        v = int(p) ** n\n        if is_pandigital(str(v)):\n            l.append([int(p), v])\n        if len(l) == k:\n            return l\n    return l[0] if len(l) == 1 else l"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'pow_root_pandigit'
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: 156224