Check if given numbers are prime numbers. 
If number N is prime ```return "Probable Prime"``` else ``` return "Composite"```. 
HINT: Upper bount is really big so you should use an efficient algorithm.

Input
  1 < N ≤ 10^(100)

Example
  prime_or_composite(2)  # should return Probable Prime
  prime_or_composite(200)  # should return Composite

```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 = '# Python3 program Miller-Rabin primality test \nimport random  \n  \n# Utility function to do \n# modular exponentiation. \n# It returns (x^y) % p \ndef power(x, y, p): \n      \n    # Initialize result \n    res = 1;  \n      \n    # Update x if it is more than or \n    # equal to p \n    x = x % p;  \n    while (y > 0): \n          \n        # If y is odd, multiply \n        # x with result \n        if (y & 1): \n            res = (res * x) % p; \n  \n        # y must be even now \n        y = y>>1; # y = y/2 \n        x = (x * x) % p; \n      \n    return res; \n  \n# This function is called \n# for all k trials. It returns \n# false if n is composite and  \n# returns false if n is \n# probably prime. d is an odd  \n# number such that d*2<sup>r</sup> = n-1 \n# for some r >= 1 \ndef miillerTest(d, n): \n      \n    # Pick a random number in [2..n-2] \n    # Corner cases make sure that n > 4 \n    a = 2 + random.randint(1, n - 4); \n  \n    # Compute a^d % n \n    x = power(a, d, n); \n  \n    if (x == 1 or x == n - 1): \n        return True; \n  \n    # Keep squaring x while one  \n    # of the following doesn\'t  \n    # happen \n    # (i) d does not reach n-1 \n    # (ii) (x^2) % n is not 1 \n    # (iii) (x^2) % n is not n-1 \n    while (d != n - 1): \n        x = (x * x) % n; \n        d *= 2; \n  \n        if (x == 1): \n            return False; \n        if (x == n - 1): \n            return True; \n  \n    # Return composite \n    return False; \n  \n# It returns false if n is  \n# composite and returns true if n \n# is probably prime. k is an  \n# input parameter that determines \n# accuracy level. Higher value of  \n# k indicates more accuracy. \ndef prime_or_composite( n, k=10): \n      \n    # Corner cases \n    if (n <= 1 or n == 4): \n        return "Composite"; \n    if (n <= 3): \n        return "Probable Prime"; \n  \n    # Find r such that n =  \n    # 2^d * r + 1 for some r >= 1 \n    d = n - 1; \n    while (d % 2 == 0): \n        d //= 2; \n  \n    # Iterate given nber of \'k\' times \n    for i in range(k): \n        if (miillerTest(d, n) == False): \n            return "Composite"\n  \n    return "Probable Prime"; '
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'prime_or_composite'
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: 5448