結果

問題 No.2313 Product of Subsequence (hard)
ユーザー lam6er
提出日時 2025-04-15 23:49:04
言語 PyPy3
(7.3.15)
結果
TLE  
実行時間 -
コード長 3,389 bytes
コンパイル時間 272 ms
コンパイル使用メモリ 82,344 KB
実行使用メモリ 187,108 KB
最終ジャッジ日時 2025-04-15 23:50:49
合計ジャッジ時間 14,449 ms
ジャッジサーバーID
（参考情報） 		judge5 / judge2
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 10 TLE * 1 -- * 16
権限があれば一括ダウンロードができます

ソースコード

diff # 

MOD = 998244353

def factorize(k):
    factors = {}
    i = 2
    while i * i <= k:
        while k % i == 0:
            factors[i] = factors.get(i, 0) + 1
            k //= i
        i += 1
    if k > 1:
        factors[k] = 1
    return factors

def main():
    import sys
    input = sys.stdin.read().split()
    ptr = 0
    N, K = int(input[ptr]), int(input[ptr+1])
    ptr += 2
    A = list(map(int, input[ptr:ptr+N]))
    ptr += N

    if K == 1:
        print((pow(2, N, MOD) - 1) % MOD)
        return

    factors = factorize(K)
    primes = list(factors.keys())
    m = len(primes)
    e = [factors[p] for p in primes]

    element_exponents = []
    for num in A:
        ex = []
        for p in primes:
            cnt = 0
            tmp = num
            while tmp % p == 0:
                cnt += 1
                tmp //= p
            ex.append(cnt)
        element_exponents.append(ex)

    inclusion_exclusion = 0

    for mask in range(1, 1 << m):
        subset_indices = []
        subset_e = []
        for i in range(m):
            if (mask >> i) & 1:
                subset_indices.append(i)
                subset_e.append(e[i])
        k = len(subset_indices)
        allowed = []
        for idx in range(N):
            valid = True
            for i in subset_indices:
                if element_exponents[idx][i] >= e[i]:
                    valid = False
                    break
            if valid:
                allowed.append(idx)
        if not allowed:
            count = 0
        else:
            state_size = 1
            for ee in subset_e:
                state_size *= ee
            if state_size > 10**6:
                continue
            multipliers = [1] * len(subset_e)
            for i in range(1, len(subset_e)):
                multipliers[i] = multipliers[i-1] * subset_e[i-1]
            dp = [0] * state_size
            dp[0] = 1
            for idx in allowed:
                ex = [element_exponents[idx][i] for i in subset_indices]
                new_dp = dp.copy()
                for state in range(state_size):
                    if dp[state] == 0:
                        continue
                    current = []
                    rem = state
                    for i in range(len(subset_e)):
                        current.append(rem % subset_e[i])
                        rem = rem // subset_e[i]
                    new_current = [current[i] + ex[i] for i in range(len(subset_e))]
                    valid = True
                    for i in range(len(subset_e)):
                        if new_current[i] >= subset_e[i]:
                            valid = False
                            break
                    if not valid:
                        continue
                    new_state = 0
                    for i in range(len(subset_e)):
                        new_state += new_current[i] * multipliers[i]
                    if new_state < state_size:
                        new_dp[new_state] = (new_dp[new_state] + dp[state]) % MOD
                dp = new_dp
            total = (sum(dp) - 1) % MOD
            count = total
        sign = (-1) ** (k + 1)
        inclusion_exclusion = (inclusion_exclusion + sign * count) % MOD

    total_subsets = (pow(2, N, MOD) - 1) % MOD
    ans = (total_subsets - inclusion_exclusion) % MOD
    print(ans)

if __name__ == '__main__':
    main()
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