#655785 (PyPy3) No.125 悪の花弁

• 問題: No.125 悪の花弁
• ユーザー: ayaoni
• 提出日時: 2021-05-09 13:12:43
• 言語: PyPy3 (7.3.15)
• 結果: AC
• 実行時間: 128 ms / 5,000 ms
• コード長: 1,438 bytes
• コンパイル時間: 353 ms
• コンパイル使用メモリ: 82,060 KB
• 実行使用メモリ: 170,112 KB
• 最終ジャッジ日時: 2024-09-18 19:26:34
• 合計ジャッジ時間: 1,661 ms
• ジャッジサーバーID （参考情報）: judge3 / judge2

ファイルパターン	結果
other	AC * 6

ソースコード

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import sys
from math import gcd
sys.setrecursionlimit(10**7)
def I(): return int(sys.stdin.readline().rstrip())
def MI(): return map(int,sys.stdin.readline().rstrip().split())
def LI(): return list(map(int,sys.stdin.readline().rstrip().split()))
def LI2(): return list(map(int,sys.stdin.readline().rstrip()))
def S(): return sys.stdin.readline().rstrip()
def LS(): return list(sys.stdin.readline().rstrip().split())
def LS2(): return list(sys.stdin.readline().rstrip())
K = I()
C = LI()
N = sum(C)
mod = 10**9+7
g = N  # g = gcd(N,C1,…,CK)
for c in C:
    g = gcd(g,c)
div = []  # gの約数
for i in range(1,g+1):
    if g % i == 0:
        div.append(i)
fac = [1]
for i in range(1,N+1):
    fac.append((fac[-1]*i) % mod)
fac_inv = [0]*(N+1)
a = pow(fac[-1],mod-2,mod)
for i in range(N,-1,-1):
    fac_inv[i] = a
    a *= i
    a %= mod
def f(n,M):
    # f(n,M) = n!/(m1!*m2!*…) (M = [m1,m2,…])
    res = fac[n]
    for m in M:
        res *= fac_inv[m]
        res %= mod
    return res
def phi(n):
    if n == 1:
        return 1
    res = n
    for i in range(2,int(n**.5)+1):
        if n % i == 0:
            res -= res//i
            while n % i == 0:
                n //= i
            if n == 1:  # 時間短縮
                break
    else:
        res -= res//n
    return res
ans = 0
for d in div:
    ans += phi(d)*f(N//d,[c//d for c in C])
    ans %= mod
ans *= pow(N,mod-2,mod)
ans %= mod
print(ans)
 
 
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