#1161690 (PyPy3) No.2313 Product of Subsequence (hard)

• 問題: No.2313 Product of Subsequence (hard)
• ユーザー: LyricalMaestro
• 提出日時: 2026-04-26 03:32:42
• 言語: PyPy3 (7.3.17)
• 結果: TLE
• 実行時間: -
• コード長: 4,320 bytes
• コンパイル時間: 499 ms
• コンパイル使用メモリ: 85,632 KB
• 実行使用メモリ: 336,900 KB
• 最終ジャッジ日時: 2026-04-26 03:33:13
• 合計ジャッジ時間: 10,004 ms
• ジャッジサーバーID （参考情報）: judge3_1 / judge1_0

ファイルパターン	結果
sample	AC * 3
other	AC * 10 TLE * 1 -- * 16

ソースコード

## https://yukicoder.me/problems/no/353

import math

MOD = 998244353


class CombinationCalculator:
    """
    modを考慮したPermutation, Combinationを計算するためのクラス
    """    
    def __init__(self, size, mod):
        self.mod = mod
        self.factorial = [0] * (size + 1)
        self.factorial[0] = 1
        for i in range(1, size + 1):
            self.factorial[i] = (i * self.factorial[i - 1]) % self.mod
        
        self.inv_factorial = [0] * (size + 1)
        self.inv_factorial[size] = pow(self.factorial[size], self.mod - 2, self.mod)

        for i in reversed(range(size)):
            self.inv_factorial[i] = ((i + 1) * self.inv_factorial[i + 1]) % self.mod

    def calc_combination(self, n, r):
        if n < 0 or n < r or r < 0:
            return 0

        if r == 0 or n == r:
            return 1
        
        ans = self.inv_factorial[n - r] * self.inv_factorial[r]
        ans %= self.mod
        ans *= self.factorial[n]
        ans %= self.mod
        return ans
    
    def calc_permutation(self, n, r):
        if n < 0 or n < r:
            return 0

        ans = self.inv_factorial[n - r]
        ans *= self.factorial[n]
        ans %= self.mod
        return ans
        

def main():
    N, K = map(int, input().split())
    A = list(map(int, input().split()))
    if K == 1:
        print((pow(2, N, MOD) - 1) % MOD)
        return

    base_k = K

    # Kを素因数分解
    sqrt_k = int(math.sqrt(K))
    k_primes = {}
    for p in range(2, sqrt_k + 1):
        if K % p == 0:
            ans = 0
            while K % p == 0:
                ans += 1
                K //= p
            k_primes[p] = ans
    if K > 1:
        k_primes[K] = 1
    
    k_primes_array = [(p, value) for p, value in k_primes.items()]
    k_primes_array.sort(key=lambda x: x[0])

    # 状態を全て定義
    def dfs(k_primes_array, index, p, p_list, p_to_list_map):
        if index == len(k_primes_array):
            xx = tuple(p_list)
            p_to_list_map[p] = xx
            return

        p0, value = k_primes_array[index]
        q = 1
        for v in range(value + 1):
            p_list.append(v)
            dfs(k_primes_array, index + 1, p * q, p_list, p_to_list_map)
            p_list.pop()
            q *= p0
        return

    p_to_list_map = {}
    dfs(k_primes_array, 0, 1, [], p_to_list_map)

    # 各種状態遷移について定義しておく
    transition = {}
    for from_p, from_p_list in p_to_list_map.items():
        for transi_p, transi_p_list in p_to_list_map.items():
            q = 1
            for j in range(len(k_primes_array)):
                p, max_v = k_primes_array[j]
                q *= p ** (min(max_v, from_p_list[j] + transi_p_list[j]))
            
            transition[(from_p, transi_p)] = q


    # 各要素について
    a_array = {}
    for a in A:
        ans = []
        q = 1
        for p, value in k_primes_array:
            x = 0
            while a % p == 0:
                x += 1
                a //= p
            x = min(value, x)
            q *= p ** x
        if q not in a_array:
            a_array[q] = 0
        a_array[q] += 1

    combi = CombinationCalculator(N, MOD)
    
    # dpで解く
    dp = {1: 1}
    for a, freq_q in a_array.items():
        new_dp = dp.copy()
        for key_p, value in dp.items():
            key_p0 = key_p

            xxx = 1
            for q in range(1, freq_q + 1):
                if key_p0 == base_k:
                    yyy = (pow(2, freq_q, MOD) - xxx) % MOD
                    if key_p0 not in new_dp:
                        new_dp[key_p0] = 0
                    new_dp[key_p0] += (value * yyy) % MOD
                    new_dp[key_p0] %= MOD
                    break

                new_key_p = transition[(key_p0, a)]
                if new_key_p not in new_dp:
                    new_dp[new_key_p] = 0
                new_dp[new_key_p] += (value * combi.calc_combination(freq_q, q)) % MOD
                new_dp[new_key_p] %= MOD

                xxx += combi.calc_combination(freq_q, q)
                xxx %= MOD
                key_p0 = new_key_p

        dp = new_dp
    
    if base_k not in dp:
        print(0)
    else:
        print(dp[base_k])



            






if __name__ == "__main__":
    main()