結果

問題 No.1923 Divisor Array
ユーザー LyricalMaestro
提出日時 2025-05-04 13:55:10
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 357 ms / 2,000 ms
コード長 3,330 bytes
コンパイル時間 445 ms
コンパイル使用メモリ 82,660 KB
実行使用メモリ 108,476 KB
最終ジャッジ日時 2025-05-04 13:55:19
合計ジャッジ時間 8,334 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge3
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ファイルパターン 結果
sample AC * 3
other AC * 51
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ソースコード

diff # 

## https://yukicoder.me/problems/no/1923

import sys

sys.setrecursionlimit(5000)

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, M, K = map(int, input().split())

    combi = CombinationCalculator(2 * max(20, M) + 1, MOD)

    # 1つの素数が分布する個数の計算

    dp = [[0] * (M + 2) for _ in range(M + 1)]
    dp[0][0] = 1
    answers = [0] * (M + 1)
    ppp = 1
    answers[0] = 1
    for num_iter in range(min(N, M)):
        ppp *= (N - num_iter)
        ppp %= MOD
        p = (ppp * combi.inv_factorial[num_iter + 1]) % MOD

        for total_index_iter in range(M + 1):
            if total_index_iter + 1 <= M:
                dp[num_iter + 1][total_index_iter + 1] += dp[num_iter][total_index_iter]
                dp[num_iter + 1][total_index_iter + 1] %= MOD
                m = min(M + 1, 2 * total_index_iter + 2)
                dp[num_iter + 1][m] -= dp[num_iter][total_index_iter]
                dp[num_iter + 1][m] %= MOD

        c = 0
        for total_index_iter in range(M + 2):
            c += dp[num_iter + 1][total_index_iter]
            c %= MOD
            dp[num_iter + 1][total_index_iter] = c
        
        for m in range(M + 1):
            answers[m] += (dp[num_iter + 1][m] * p) % MOD
            answers[m] %= MOD

    def dfs(total_choced, M, answers, ans, divisor_num, choiced):
        if total_choced == choiced:
            return ans
        
        if M < divisor_num:
            return 0

        ans_0 = 0
        max_m = M // divisor_num
        for m in reversed(range(1, max_m)):
            if (m + 1) * divisor_num <= M:
                ans1 = dfs(total_choced, M, answers, (ans * answers[m]) % MOD, divisor_num * (m + 1), choiced + 1)
                ans_0 += ans1
                ans_0 %= MOD
        return ans_0

    ddd = 1    
    answer = 1
    for choce in range(1, min(15, K) + 1):
        ddd *= (K - choce + 1)
        ddd %= MOD
        d = (ddd * combi.inv_factorial[choce]) % MOD

        ans0 = dfs(choce, M, answers, 1, 1, 0)
        answer += (ans0 * d) % MOD
        answer %= MOD
    print(answer)







        

        

        







if __name__ == "__main__":
    main()
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