# Python Miller-Rabin implementation

import random
import lib.arithmetics as arithm

def get_d_and_s(n: int) -> (int, int):
    d = n - 1
    s = 0
    while d % 2 == 0:
        d //= 2
        s += 1
    return (d, s)

def rabin_witness(n: int, a: int) -> bool:
    d, s = get_d_and_s(n)
    x = arithm.modpow(a, d, n)
    if x == 1 or x == n - 1:
        return False
    for _ in range(s - 1):
        x = arithm.modpow(x, 2, n)
        if x == n - 1:
            return False
    return True

def miller_rabin(n: int, k: int) -> bool:
    if n < 3: return False
    for _ in range(k):
        a = random.randint(2, n - 1)
        if rabin_witness(n, a): return False
    return True

def is_prime(n: int) -> bool:
    return miller_rabin(n, 25)

def get_random_prime(n: int) -> int:
    a = random.randint(2**(n-1), 2**(n) - 1)
    while not is_prime(a):
        a = random.randint(2**(n-1), 2**(n) - 1)
    return a