循环表上可以直接除以2吗？先看它有没有把不同位置挤在一起

"""Invert a cyclic multiplier only when it preserves every residue uniquely."""
import math
import json


def inverse(a, modulus):
    if any(type(x) is not int for x in (a, modulus)) or modulus < 2:
        raise ValueError("integer a and modulus >= 2 required")
    a %= modulus
    old_r, r, old_s, s = a, modulus, 1, 0
    trace = []
    while r:
        quotient = old_r // r
        trace.append({"left": old_r, "right": r, "quotient": quotient})
        old_r, r = r, old_r - quotient * r
        old_s, s = s, old_s - quotient * s
    if old_r != 1:
        return None, trace
    return old_s % modulus, trace


def all_solutions(a, b, modulus):
    # Deliberately independent bounded oracle, no gcd, pow or Euclidean steps.
    if not 2 <= modulus <= 100:
        raise ValueError("enumeration limited to moduli 2..100")
    return [x for x in range(modulus) if (a * x - b) % modulus == 0]


def main():
    checks, cases = 0, 0
    def check(ok):
        nonlocal checks
        if not ok:
            raise AssertionError("modular check failed")
        checks += 1
    for modulus in range(2, 41):
        for a in range(-2 * modulus, 2 * modulus + 1):
            found, _ = inverse(a, modulus)
            answers = all_solutions(a, 1, modulus)
            check(answers == ([] if found is None else [found]))
            check((found is not None) == (math.gcd(a, modulus) == 1))
            if found is not None:
                check(found == pow(a, -1, modulus))
                for b in (0, 1, modulus - 1):
                    check(all_solutions(a, b, modulus) == [(b * found) % modulus])
            else:
                try:
                    pow(a, -1, modulus)
                except ValueError:
                    check(True)
                else:
                    raise AssertionError("pow accepted noninvertible base")
            cases += 1
    for args in [(1, 1), (1, 0), (True, 7), (1, 7.0)]:
        try:
            inverse(*args)
        except ValueError:
            check(True)
        else:
            raise AssertionError("invalid modulus accepted")
    answer, trace = inverse(5, 12)
    check(answer == 5)
    check(all_solutions(2, 4, 6) == [2, 5])
    check(all_solutions(2, 1, 6) == [])
    print(json.dumps({"checks_passed": checks, "a_modulus_cases": cases,
                      "clock_5x_mod12_equals7": (7 * answer) % 12,
                      "inverse_5_mod12": answer, "euclid_trace": trace,
                      "2x_mod6_equals4": all_solutions(2, 4, 6),
                      "2x_mod6_equals1": all_solutions(2, 1, 6),
                      "scope": "integer arithmetic; no cryptographic constant-time or key generation guarantee"}, indent=2))


if __name__ == "__main__":
    main()