AtCoder Beginner Contest 349 F問題メモ

from collections import Counter

# Pollard's rho algorithm
# https://qiita.com/t_fuki/items/7cd50de54d3c5d063b4a

def gcd(a, b):
    while a:
        a, b = b % a, a
    return b


def is_prime(n):
    if n == 2:
        return 1
    if n == 1 or n % 2 == 0:
        return 0

    m = n - 1
    lsb = m & -m
    s = lsb.bit_length() - 1
    d = m // lsb

    test_numbers = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37]

    for a in test_numbers:
        if a == n:
            continue
        x = pow(a, d, n)
        r = 0
        if x == 1:
            continue
        while x != m:
            x = pow(x, 2, n)
            r += 1
            if x == 1 or r == s:
                return 0
    return 1


def find_prime_factor(n):
    if n % 2 == 0:
        return 2

    m = int(n ** 0.125) + 1

    for c in range(1, n):
        f = lambda a: (pow(a, 2, n) + c) % n
        y = 0
        g = q = r = 1
        k = 0
        while g == 1:
            x = y
            while k < 3 * r // 4:
                y = f(y)
                k += 1
            while k < r and g == 1:
                ys = y
                for _ in range(min(m, r - k)):
                    y = f(y)
                    q = q * abs(x - y) % n
                g = gcd(q, n)
                k += m
            k = r
            r *= 2
        if g == n:
            g = 1
            y = ys
            while g == 1:
                y = f(y)
                g = gcd(abs(x - y), n)
        if g == n:
            continue
        if is_prime(g):
            return g
        elif is_prime(n // g):
            return n // g
        else:
            return find_prime_factor(g)
    print('Hello', n)


def factorize(n):
    res = {}
    while not is_prime(n) and n > 1:  # nが合成数である間nの素因数の探索を繰り返す
        p = find_prime_factor(n)
        s = 0
        while n % p == 0:  # nが素因数pで割れる間割り続け、出力に追加
            n //= p
            s += 1
        res[p] = s
    if n > 1:  # n>1であればnは素数なので出力に追加
        res[n] = 1
    return res


n, m = map(int, input().split())
aaa = list(map(int, input().split()))
MOD = 998244353

if m == 1:
    ans = pow(2, aaa.count(1), MOD) - 1
    print(ans)
    exit()

fct = factorize(m)
s = len(fct)
mask = (1 << s) - 1
fct = [(i, pow(p, q)) for i, (p, q) in enumerate(fct.items())]

bbb = Counter()
for a in aaa:
    if m % a != 0:
        continue
    tmp = 0
    for i, pq in fct:
        if a % pq == 0:
            tmp |= 1 << i
    bbb[tmp] += 1

init = pow(2, bbb[0], MOD)
del bbb[0]

ss = 1 << s
dp = [0] * ss
dp[0] = init

for bit, cnt in bbb.items():
    pat = pow(2, cnt, MOD) - 1
    for i in range(ss - 1, -1, -1):
        dp[i | bit] += dp[i] * pat
        dp[i | bit] %= MOD

print(dp[mask])