結果
問題 | No.1039 Project Euler でやれ |
ユーザー |
![]() |
提出日時 | 2020-04-24 23:42:24 |
言語 | Python3 (3.13.1 + numpy 2.2.1 + scipy 1.14.1) |
結果 |
RE
(最新)
AC
(最初)
|
実行時間 | - |
コード長 | 2,301 bytes |
コンパイル時間 | 270 ms |
コンパイル使用メモリ | 12,928 KB |
実行使用メモリ | 44,208 KB |
最終ジャッジ日時 | 2024-11-08 02:59:59 |
合計ジャッジ時間 | 13,796 ms |
ジャッジサーバーID (参考情報) |
judge5 / judge3 |
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ファイルパターン | 結果 |
---|---|
sample | RE * 2 |
other | RE * 18 |
ソースコード
import sysread = sys.stdin.buffer.readreadline = sys.stdin.buffer.readlinereadlines = sys.stdin.buffer.readlinesimport numpy as npfrom functools import lru_cacheMOD = 10 ** 9 + 7U = 10 ** 3 + 10is_prime = np.zeros(U, np.bool)is_prime[2] = 1is_prime[3::2] = 1for p in range(3, U, 2):if p * p >= U:breakif is_prime[p]:is_prime[p * p:: p + p] = 0primes = np.where(is_prime)[0]def cumprod(A, MOD=MOD):L = len(A)Lsq = int(L**.5 + 1)A = np.resize(A, Lsq**2).reshape(Lsq, Lsq)for n in range(1, Lsq):A[:, n] *= A[:, n - 1]A[:, n] %= MODfor n in range(1, Lsq):A[n] *= A[n - 1, -1]A[n] %= MODreturn A.ravel()[:L]def make_fact(U, MOD=MOD):x = np.arange(U, dtype=np.int64)x[0] = 1fact = cumprod(x, MOD)fact.flags.writeable = Falsereturn factdef factor(M):pf = primes[M % primes == 0]for p in pf:e = 0while M % p == 0:M //= pe += 1yield (int(p), e)if M > 1:yield (int(M), 1)@lru_cache(None)def GL(p, n):# count the element of GL(n,F_p)x = 1for i in range(n):x *= (p ** n - p ** i)x %= MODreturn x % MODdef Aut(p, e, partition):# count Aut(prod Z/p^{n_i})x = 1smaller = 0for i in range(1, e + 1):n = sum(k == i for k in partition)x *= GL(p, n)x *= pow(p, (i - 1) * n * n, MOD)x *= pow(p, smaller * n, MOD)m = sum(k > i for k in partition)x *= pow(p, i * m * n, MOD)smaller += n * ireturn x % MODdef make_partitions(N, largest=None):if N == 0:yield []returnif largest is None:largest = Nif largest > N:largest = Nfor i in range(largest, 0, -1):for p in make_partitions(N - i, i):yield p + [i]def compute_p_part(p, e):# sum(1 / Aut)x = 0for par in make_partitions(e):aut = Aut(p, e, par)x += pow(aut, MOD - 2, MOD)x %= MODreturn xdef solve(M):fact = make_fact(M + 10)x = 1for p, e in factor(M):x *= compute_p_part(p, e)x %= MODx *= fact[M]return x % MODM = int(read())print(solve(M))