#832294 (PyPy3) No.2578 Jewelry Store

• 問題: No.2578 Jewelry Store
• ユーザー: suisen
• 提出日時: 2023-01-13 17:55:44
• 言語: PyPy3 (7.3.15)
• 結果: AC
• 実行時間: 2,066 ms / 3,500 ms
• コード長: 3,360 bytes
• コンパイル時間: 438 ms
• コンパイル使用メモリ: 82,512 KB
• 実行使用メモリ: 137,260 KB
• 最終ジャッジ日時: 2024-09-27 00:36:47
• 合計ジャッジ時間: 18,068 ms
• ジャッジサーバーID （参考情報）: judge3 / judge5

ファイルパターン	結果
other	AC * 54

ソースコード

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import sys
from typing import List
from math import gcd
input = sys.stdin.readline
# https://qiita.com/Kiri8128/items/eca965fe86ea5f4cbb98
class PrimeFactorize:
    @staticmethod
    def __isPrimeMR(n: int):
        d = n - 1
        d = d // (d & -d)
        L = [2]
        for a in L:
            t = d
            y = pow(a, t, n)
            if y == 1: continue
            while y != n - 1:
                y = (y * y) % n
                if y == 1 or t == n - 1: return 0
                t <<= 1
        return 1
    @staticmethod
    def __findFactorRho(n: int):
        m = 1 << n.bit_length() // 8
        for c in range(1, 99):
            f = lambda x: (x * x + c) % n
            y, r, q, g = 2, 1, 1, 1
            x = ys = y
            while g == 1:
                x = y
                for i in range(r):
                    y = f(y)
                k = 0
                while k < r and g == 1:
                    ys = y
                    for i in range(min(m, r - k)):
                        y = f(y)
                        q = q * abs(x - y) % n
                    g = gcd(q, n)
                    k += m
                r <<= 1
            if g == n:
                g = 1
                while g == 1:
                    ys = f(ys)
                    g = gcd(abs(x - ys), n)
            if g < n:
                if PrimeFactorize.__isPrimeMR(g): return g
                elif PrimeFactorize.__isPrimeMR(n // g): return n // g
                return PrimeFactorize.__findFactorRho(g)
    @staticmethod
    def primeFactor(n):
        i = 2
        ret = {}
        rhoFlg = 0
        while i*i <= n:
            k = 0
            while n % i == 0:
                n //= i
                k += 1
            if k: ret[i] = k
            i += 1 + i % 2
            if i == 101 and n >= 2 ** 20:
                while n > 1:
                    if PrimeFactorize.__isPrimeMR(n):
                        ret[n], n = 1, 1
                    else:
                        rhoFlg = 1
                        j = PrimeFactorize.__findFactorRho(n)
                        k = 0
                        while n % j == 0:
                            n //= j
                            k += 1
                        ret[j] = k
        if n > 1: ret[n] = 1
        if rhoFlg: ret = {x: ret[x] for x in sorted(ret)}
        return ret
P = 998244353
t, m = map(int, input().split())
pf = PrimeFactorize.primeFactor(m).keys()
k = len(pf)
parity = [(-1) ** bin(s).count('1') for s in range(1 << k)]
def supset_zeta_product(f: List[int]):
    block = 1
    while block < 1 << k:
        offset = 0
        while offset < 1 << k:
            for i in range(offset, offset + block):
                f[i] = f[i + block] * f[i] % P
            offset += 2 * block
        block <<= 1
def solve():
    _, x0, c, d = map(int, input().split())
    prod = [1] * (1 << k)
    wi = x0
    for ai in map(int, input().split()):
        q, r = divmod(m, ai)
        if r == 0:
            t = 0
            for j, p in enumerate(pf):
                t |= (q % p == 0) << j
            prod[t] = prod[t] * (1 + wi) % P
        wi = (c * wi + d) % P
    
    supset_zeta_product(prod)
    ans = 0
    for s in range(1 << k):
        ans += parity[s] * prod[s]
    if m == 1:
        ans -= 1
    print(ans % P)
for _ in range(t):
    solve()
 
 
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