結果

問題 No.2959 Dolls' Tea Party
ユーザー gew1fw
提出日時 2025-06-12 21:18:55
言語 PyPy3
(7.3.15)
結果
TLE  
実行時間 -
コード長 3,663 bytes
コンパイル時間 282 ms
コンパイル使用メモリ 81,912 KB
実行使用メモリ 257,400 KB
最終ジャッジ日時 2025-06-12 21:19:14
合計ジャッジ時間 7,515 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 * 4
other AC * 5 TLE * 1 -- * 27
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 # 

import sys
MOD = 998244353

def main():
    N, K = map(int, sys.stdin.readline().split())
    A = list(map(int, sys.stdin.readline().split()))
    
    # Precompute factorial and inverse factorial up to 1300
    max_m = 1300
    fact = [1] * (max_m + 1)
    for i in range(1, max_m + 1):
        fact[i] = fact[i-1] * i % MOD
    inv_fact = [1] * (max_m + 1)
    inv_fact[max_m] = pow(fact[max_m], MOD-2, MOD)
    for i in range(max_m-1, -1, -1):
        inv_fact[i] = inv_fact[i+1] * (i+1) % MOD
    
    # Function to multiply two polynomials up to degree m
    def multiply_poly(a, b, m):
        res = [0]*(m+1)
        for i in range(len(a)):
            if a[i] == 0:
                continue
            for j in range(len(b)):
                if i + j > m:
                    break
                res[i+j] = (res[i+j] + a[i] * b[j]) % MOD
        return res
    
    # Function to compute poly^e using exponentiation by squaring, up to degree m
    def pow_poly(poly, e, m):
        result = [1]  # Identity element
        current = poly.copy()
        while e > 0:
            if e % 2 == 1:
                result = multiply_poly(result, current, m)
            current = multiply_poly(current, current, m)
            e = e // 2
        return result
    
    # Get all divisors of K
    def get_divisors(n):
        divisors = []
        for i in range(1, int(n**0.5)+1):
            if n % i == 0:
                divisors.append(i)
                if i != n // i:
                    divisors.append(n//i)
        divisors.sort()
        return divisors
    
    divisors = get_divisors(K)
    phi = {}
    for d in divisors:
        # Compute Euler's totient function for d
        temp = d
        prime_factors = {}
        x = d
        for i in range(2, int(x**0.5)+1):
            if x % i == 0:
                prime_factors[i] = 0
                while x % i == 0:
                    prime_factors[i] += 1
                    x = x // i
        if x > 1:
            prime_factors[x] = 1
        phi_val = 1
        for p, cnt in prime_factors.items():
            phi_val *= (p**(cnt) - p**(cnt-1))
        phi[d] = phi_val
    
    inv_K = pow(K, MOD-2, MOD)
    total_ans = 0
    
    for d in divisors:
        m = K // d
        if m > max_m:
            continue  # since max_m is 1300 and K <=1300, m can't exceed 1300
        
        c_list = []
        sum_c = 0
        for a in A:
            c = a // d
            c = min(c, m)
            c_list.append(c)
            sum_c += c
        if sum_c < m:
            continue
        
        t_high = 0
        list_low = []
        for c in c_list:
            if c >= m:
                t_high += 1
            else:
                list_low.append(c)
        
        # Compute P_high = (sum_{k=0}^m x^k/k! )^t_high
        if t_high == 0:
            P_high = [1] + [0]*m
        else:
            base = [0]*(m+1)
            for k in range(m+1):
                base[k] = inv_fact[k]
            P_high = pow_poly(base, t_high, m)
        
        # Compute P_low
        P_low = [1] + [0]*m
        for c in list_low:
            current_poly = [0]*(c+1)
            for k in range(c+1):
                current_poly[k] = inv_fact[k]
            P_low = multiply_poly(P_low, current_poly, m)
        
        # Multiply P_high and P_low
        total = multiply_poly(P_high, P_low, m)
        if len(total) <= m:
            coeff = 0
        else:
            coeff = total[m]
        f_d = coeff * fact[m] % MOD
        
        total_ans = (total_ans + phi[d] * f_d) % MOD
    
    ans = total_ans * inv_K % MOD
    print(ans)

if __name__ == '__main__':
    main()
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