#!/usr/bin/env python3

"""Signature et vérification de signature avec RSA"""

import sys


def main() -> None:
    """Call functions dependending on args"""

    if len(sys.argv) == 1:
        command = input("command ('sign' or 'verify'): ")
    else:
        command = sys.argv[1]
    if command == "sign":
        ac = int(input("AC : "))
        d = int(input("d : "))
        nd = int(input("nd : "))
        e = int(input("e : "))
        ne = int(input("ne : "))
        s = sign(ac, d, e, nd, ne)
        print(s)
    elif command == "verify":
        s = int(input("S : "))
        ac = int(input("AC : "))
        d = int(input("d : "))
        nd = int(input("nd : "))
        e = int(input("e : "))
        ne = int(input("ne : "))
        if verify(s, ac, d, e, nd, ne):
            print("YES")
        else:
            print("NO")


def sign(ac: int, d: int, e: int, nd: int, ne: int) -> int:
    """Produce a signature"""

    if nd <= ne:
        return pow(pow(ac, d, nd), e, ne)
    return pow(pow(ac, e, ne), d, nd)


def verify(s: int, ac: int, d: int, e: int, nd: int, ne: int) -> bool:
    """Verify a signature"""

    if nd >= ne:
        maybe = pow(pow(s, d, nd), e, ne)
    else:
        maybe = pow(pow(s, e, ne), d, nd)
    print(f"Found AC = {maybe}")
    return maybe == ac

if __name__ == "__main__":
    main()