結果

問題 No.125 悪の花弁
ユーザー hashiryo
提出日時 2024-02-08 21:39:47
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 41 ms / 5,000 ms
コード長 15,880 bytes
コンパイル時間 2,979 ms
コンパイル使用メモリ 215,564 KB
最終ジャッジ日時 2025-02-19 02:54:02
ジャッジサーバーID
（参考情報） 		judge5 / judge2
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ファイルパターン 結果
other AC * 6
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// #define _GLIBCXX_DEBUG
#include <bits/stdc++.h>
// clang-format off
std::ostream&operator<<(std::ostream&os,std::int8_t x){return os<<(int)x;}
std::ostream&operator<<(std::ostream&os,std::uint8_t x){return os<<(int)x;}
std::ostream&operator<<(std::ostream&os,const __int128_t &v){if(!v)os<<"0";__int128_t tmp=v<0?(os<<"-",-v):v;std::string s;while(tmp)s+='0'+(tmp%10
    ),tmp/=10;return std::reverse(s.begin(),s.end()),os<<s;}
std::ostream&operator<<(std::ostream&os,const __uint128_t &v){if(!v)os<<"0";__uint128_t tmp=v;std::string s;while(tmp)s+='0'+(tmp%10),tmp/=10;return 
    std::reverse(s.begin(),s.end()),os<<s;}
#define checkpoint() (void(0))
#define debug(...) (void(0))
#define debugArray(x,n) (void(0))
#define debugMatrix(x,h,w) (void(0))
// clang-format on
#include <type_traits>
template <class Int> constexpr inline Int mod_inv(Int a, Int mod) {
 static_assert(std::is_signed_v<Int>);
 Int x= 1, y= 0, b= mod;
 for (Int q= 0, z= 0; b;) z= x, x= y, y= z - y * (q= a / b), z= a, a= b, b= z - b * q;
 return assert(a == 1), x < 0 ? mod - (-x) % mod : x % mod;
}
namespace math_internal {
using namespace std;
using u8= unsigned char;
using u32= unsigned;
using i64= long long;
using u64= unsigned long long;
using u128= __uint128_t;
#define CE constexpr
#define IL inline
#define NORM \
 if (n >= mod) n-= mod; \
 return n
#define PLUS(U, M) \
 CE IL U plus(U l, U r) const { return l+= r, l < (M) ? l : l - (M); }
#define DIFF(U, C, M) \
 CE IL U diff(U l, U r) const { return l-= r, l >> C ? l + (M) : l; }
#define SGN(U) \
 static CE IL U set(U n) { return n; } \
 static CE IL U get(U n) { return n; } \
 static CE IL U norm(U n) { return n; }
template <class u_t, class du_t, u8 B, u8 A> struct MP_Mo {
 u_t mod;
 CE MP_Mo(): mod(0), iv(0), r2(0) {}
 CE MP_Mo(u_t m): mod(m), iv(inv(m)), r2(-du_t(mod) % mod) {}
 CE IL u_t mul(u_t l, u_t r) const { return reduce(du_t(l) * r); }
 PLUS(u_t, mod << 1)
 DIFF(u_t, A, mod << 1)
 CE IL u_t set(u_t n) const { return mul(n, r2); }
 CE IL u_t get(u_t n) const {
  n= reduce(n);
  NORM;
 }
 CE IL u_t norm(u_t n) const { NORM; }
private:
 u_t iv, r2;
 static CE u_t inv(u_t n, int e= 6, u_t x= 1) { return e ? inv(n, e - 1, x * (2 - x * n)) : x; }
 CE IL u_t reduce(const du_t &w) const { return u_t(w >> B) + mod - ((du_t(u_t(w) * iv) * mod) >> B); }
};
struct MP_Na {
 u32 mod;
 CE MP_Na(): mod(0){};
 CE MP_Na(u32 m): mod(m) {}
 CE IL u32 mul(u32 l, u32 r) const { return u64(l) * r % mod; }
 PLUS(u32, mod) DIFF(u32, 31, mod) SGN(u32)
};
struct MP_Br {  // mod < 2^31
 u32 mod;
 CE MP_Br(): mod(0), s(0), x(0) {}
 CE MP_Br(u32 m): mod(m), s(95 - __builtin_clz(m - 1)), x(((u128(1) << s) + m - 1) / m) {}
 CE IL u32 mul(u32 l, u32 r) const { return rem(u64(l) * r); }
 PLUS(u32, mod) DIFF(u32, 31, mod) SGN(u32) private: u8 s;
 u64 x;
 CE IL u64 quo(u64 n) const { return (u128(x) * n) >> s; }
 CE IL u32 rem(u64 n) const { return n - quo(n) * mod; }
};
struct MP_Br2 {  // 2^20 < mod <= 2^41
 u64 mod;
 CE MP_Br2(): mod(0), x(0) {}
 CE MP_Br2(u64 m): mod(m), x((u128(1) << 84) / m) {}
 CE IL u64 mul(u64 l, u64 r) const { return rem(u128(l) * r); }
 PLUS(u64, mod << 1)
 DIFF(u64, 63, mod << 1)
 static CE IL u64 set(u64 n) { return n; }
 CE IL u64 get(u64 n) const { NORM; }
 CE IL u64 norm(u64 n) const { NORM; }
private:
 u64 x;
 CE IL u128 quo(const u128 &n) const { return (n * x) >> 84; }
 CE IL u64 rem(const u128 &n) const { return n - quo(n) * mod; }
};
struct MP_D2B1 {
 u8 s;
 u64 mod, d, v;
 CE MP_D2B1(): s(0), mod(0), d(0), v(0) {}
 CE MP_D2B1(u64 m): s(__builtin_clzll(m)), mod(m), d(m << s), v(u128(-1) / d) {}
 CE IL u64 mul(u64 l, u64 r) const { return rem((u128(l) * r) << s) >> s; }
 PLUS(u64, mod) DIFF(u64, 63, mod) SGN(u64) private: CE IL u64 rem(const u128 &u) const {
  u128 q= (u >> 64) * v + u;
  u64 r= u64(u) - (q >> 64) * d - d;
  if (r > u64(q)) r+= d;
  if (r >= d) r-= d;
  return r;
 }
};
template <class u_t, class MP> CE u_t pow(u_t x, u64 k, const MP &md) {
 for (u_t ret= md.set(1);; x= md.mul(x, x))
  if (k & 1 ? ret= md.mul(ret, x) : 0; !(k>>= 1)) return ret;
}
#undef NORM
#undef PLUS
#undef DIFF
#undef SGN
#undef CE
}
namespace math_internal {
struct m_b {};
struct s_b: m_b {};
}
template <class mod_t> constexpr bool is_modint_v= std::is_base_of_v<math_internal::m_b, mod_t>;
template <class mod_t> constexpr bool is_staticmodint_v= std::is_base_of_v<math_internal::s_b, mod_t>;
namespace math_internal {
#define CE constexpr
template <class MP, u64 MOD> struct SB: s_b {
protected:
 static CE MP md= MP(MOD);
};
template <class Int, class U, class B> struct MInt: public B {
 using Uint= U;
 static CE inline auto mod() { return B::md.mod; }
 CE MInt(): x(0) {}
 template <class T, typename= enable_if_t<is_modint_v<T> && !is_same_v<T, MInt>>> CE MInt(T v): x(B::md.set(v.val() % B::md.mod)) {}
 CE MInt(__int128_t n): x(B::md.set((n < 0 ? ((n= (-n) % B::md.mod) ? B::md.mod - n : n) : n % B::md.mod))) {}
 CE MInt operator-() const { return MInt() - *this; }
#define FUNC(name, op) \
 CE MInt name const { \
  MInt ret; \
  return ret.x= op, ret; \
 }
 FUNC(operator+(const MInt & r), B::md.plus(x, r.x))
 FUNC(operator-(const MInt & r), B::md.diff(x, r.x))
 FUNC(operator*(const MInt & r), B::md.mul(x, r.x))
 FUNC(pow(u64 k), math_internal::pow(x, k, B::md))
#undef FUNC
 CE MInt operator/(const MInt& r) const { return *this * r.inv(); }
 CE MInt& operator+=(const MInt& r) { return *this= *this + r; }
 CE MInt& operator-=(const MInt& r) { return *this= *this - r; }
 CE MInt& operator*=(const MInt& r) { return *this= *this * r; }
 CE MInt& operator/=(const MInt& r) { return *this= *this / r; }
 CE bool operator==(const MInt& r) const { return B::md.norm(x) == B::md.norm(r.x); }
 CE bool operator!=(const MInt& r) const { return !(*this == r); }
 CE bool operator<(const MInt& r) const { return B::md.norm(x) < B::md.norm(r.x); }
 CE inline MInt inv() const { return mod_inv<Int>(val(), B::md.mod); }
 CE inline Uint val() const { return B::md.get(x); }
 friend ostream& operator<<(ostream& os, const MInt& r) { return os << r.val(); }
 friend istream& operator>>(istream& is, MInt& r) {
  i64 v;
  return is >> v, r= MInt(v), is;
 }
private:
 Uint x;
};
template <u64 MOD> using ModInt= conditional_t < (MOD < (1 << 30)) & MOD, MInt<int, u32, SB<MP_Mo<u32, u64, 32, 31>, MOD>>, conditional_t < (MOD < 
    (1ull << 62)) & MOD, MInt<i64, u64, SB<MP_Mo<u64, u128, 64, 63>, MOD>>, conditional_t<MOD<(1u << 31), MInt<int, u32, SB<MP_Na, MOD>>, 
    conditional_t<MOD<(1ull << 32), MInt<i64, u32, SB<MP_Na, MOD>>, conditional_t<MOD <= (1ull << 41), MInt<i64, u64, SB<MP_Br2, MOD>>, MInt<i64, u64
    , SB<MP_D2B1, MOD>>>>>>>;
#undef CE
}
using math_internal::ModInt;
namespace math_internal {
template <class Uint, class MP, u64... args> constexpr bool miller_rabin(Uint n) {
 const MP md(n);
 const Uint s= __builtin_ctzll(n - 1), d= n >> s, one= md.set(1), n1= md.norm(md.set(n - 1));
 for (auto a: {args...})
  if (Uint b= a % n; b)
   if (Uint p= md.norm(pow(md.set(b), d, md)); p != one)
    for (int i= s; p != n1; p= md.norm(md.mul(p, p)))
     if (!(--i)) return 0;
 return 1;
}
constexpr bool is_prime(u64 n) {
 if (n < 2 || n % 6 % 4 != 1) return (n | 1) == 3;
 if (n < (1 << 30)) return miller_rabin<u32, MP_Mo<u32, u64, 32, 31>, 2, 7, 61>(n);
 if (n < (1ull << 62)) return miller_rabin<u64, MP_Mo<u64, u128, 64, 63>, 2, 325, 9375, 28178, 450775, 9780504, 1795265022>(n);
 return miller_rabin<u64, MP_D2B1, 2, 325, 9375, 28178, 450775, 9780504, 1795265022>(n);
}
}
using math_internal::is_prime;
template <class Int> constexpr int bsf(Int a) {
 if constexpr (sizeof(Int) == 16) {
  uint64_t lo= a & uint64_t(-1);
  return lo ? __builtin_ctzll(lo) : 64 + __builtin_ctzll(a >> 64);
 } else if constexpr (sizeof(Int) == 8) return __builtin_ctzll(a);
 else return __builtin_ctz(a);
}
template <class Int> constexpr Int binary_gcd(Int a, Int b) {
 if (a == 0 || b == 0) return a + b;
 int n= bsf(a), m= bsf(b), s= 0;
 for (a>>= n, b>>= m; a != b;) {
  Int d= a - b;
  bool f= a > b;
  s= bsf(d), b= f ? b : a, a= (f ? d : -d) >> s;
 }
 return a << std::min(n, m);
}
namespace math_internal {
template <class T> constexpr void bubble_sort(T *bg, T *ed) {
 for (int sz= ed - bg, i= 0; i < sz; i++)
  for (int j= sz; --j > i;)
   if (auto tmp= bg[j - 1]; bg[j - 1] > bg[j]) bg[j - 1]= bg[j], bg[j]= tmp;
}
template <class T, size_t _Nm> struct ConstexprArray {
 constexpr size_t size() const { return sz; }
 constexpr auto &operator[](int i) const { return dat[i]; }
 constexpr auto *begin() const { return dat; }
 constexpr auto *end() const { return dat + sz; }
protected:
 T dat[_Nm]= {};
 size_t sz= 0;
 friend ostream &operator<<(ostream &os, const ConstexprArray &r) {
  os << "[";
  for (size_t i= 0; i < r.sz; ++i) os << r[i] << ",]"[i == r.sz - 1];
  return os;
 }
};
class Factors: public ConstexprArray<pair<u64, uint16_t>, 16> {
 template <class Uint, class MP> static constexpr Uint rho(Uint n, Uint c) {
  const MP md(n);
  auto f= [&md, n, c](Uint x) { return md.plus(md.mul(x, x), c); };
  const Uint m= 1LL << (__lg(n) / 5);
  Uint x= 1, y= md.set(2), z= 1, q= md.set(1), g= 1;
  for (Uint r= 1, i= 0; g == 1; r<<= 1) {
   for (x= y, i= r; i--;) y= f(y);
   for (Uint k= 0; k < r && g == 1; g= binary_gcd(md.get(q), n), k+= m)
    for (z= y, i= min(m, r - k); i--;) y= f(y), q= md.mul(q, md.diff(y, x));
  }
  if (g == n) do {
    z= f(z), g= binary_gcd(md.get(md.diff(z, x)), n);
   } while (g == 1);
  return g;
 }
 static constexpr u64 find_prime_factor(u64 n) {
  if (is_prime(n)) return n;
  for (u64 i= 100; i--;)
   if (n= n < (1 << 30) ? rho<u32, MP_Mo<u32, u64, 32, 31>>(n, i + 1) : n < (1ull << 62) ? rho<u64, MP_Mo<u64, u128, 64, 63>>(n, i + 1) : rho<u64, 
       MP_D2B1>(n, i + 1); is_prime(n)) return n;
  return 0;
 }
 constexpr void init(u64 n) {
  for (u64 p= 2; p < 98 && p * p <= n; ++p)
   if (n % p == 0)
    for (dat[sz++].first= p; n % p == 0;) n/= p, ++dat[sz - 1].second;
  for (u64 p= 0; n > 1; dat[sz++].first= p)
   for (p= find_prime_factor(n); n % p == 0;) n/= p, ++dat[sz].second;
 }
public:
 constexpr Factors()= default;
 constexpr Factors(u64 n) { init(n), bubble_sort(dat, dat + sz); }
};
}  // namespace math_internal
using math_internal::Factors;
constexpr uint64_t totient(const Factors &f) {
 uint64_t ret= 1, i= 0;
 for (auto [p, e]: f)
  for (ret*= p - 1, i= e; --i;) ret*= p;
 return ret;
}
constexpr auto totient(uint64_t n) { return totient(Factors(n)); }
template <class Uint= uint64_t> std::vector<Uint> enumerate_divisors(const Factors &f) {
 int k= 1;
 for (auto [p, e]: f) k*= e + 1;
 std::vector<Uint> ret(k, 1);
 k= 1;
 for (auto [p, e]: f) {
  int sz= k;
  for (Uint pw= 1; pw*= p, e--;)
   for (int j= 0; j < sz;) ret[k++]= ret[j++] * pw;
 }
 return ret;
}
template <class Uint> std::vector<Uint> enumerate_divisors(Uint n) { return enumerate_divisors<Uint>(Factors(n)); }
template <class T> struct ArrayOnDivisors {
 uint64_t n;
 uint8_t shift;
 std::vector<int> os, id;
 std::vector<std::pair<uint64_t, T>> dat;
 unsigned hash(uint64_t i) const { return (i * 11995408973635179863ULL) >> shift; }
#define _UP for (int j= k; j < a; ++j)
#define _DWN for (int j= a; j-- > k;)
#define _OP(J, K, op) dat[i + J].second op##= dat[i + K].second
#define _FUN(J, K, name) name(dat[i + J].second, dat[i + K].second)
#define _ZETA(op) \
 int k= 1; \
 for (auto [p, e]: factors) { \
  int a= k * (e + 1); \
  for (int i= 0, d= dat.size(); i < d; i+= a) op; \
  k= a; \
 }
public:
 Factors factors;
 template <class Uint> ArrayOnDivisors(uint64_t N, const Factors &factors, const std::vector<Uint> &divisors): n(N), shift(__builtin_clzll(divisors
     .size()) - 1), os((1 << (64 - shift)) + 1), id(divisors.size()), dat(divisors.size()), factors(factors) {
  for (int i= divisors.size(); i--;) dat[i].first= divisors[i];
  for (auto d: divisors) ++os[hash(d)];
  std::partial_sum(os.begin(), os.end(), os.begin());
  for (int i= divisors.size(); i--;) id[--os[hash(divisors[i])]]= i;
 }
 ArrayOnDivisors(uint64_t N, const Factors &factors): ArrayOnDivisors(N, factors, enumerate_divisors(factors)) {}
 ArrayOnDivisors(uint64_t N): ArrayOnDivisors(N, Factors(N)) {}
 T &operator[](uint64_t i) {
  assert(i && n % i == 0);
  for (unsigned a= hash(i), j= os[a]; j < os[a + 1]; ++j)
   if (auto &[d, v]= dat[id[j]]; d == i) return v;
  assert(0);
 }
 size_t size() const { return dat.size(); }
 auto begin() { return dat.begin(); }
 auto begin() const { return dat.begin(); }
 auto end() { return dat.begin() + os.back(); }
 auto end() const { return dat.begin() + os.back(); }
 /* f -> g s.t. g(n) = sum_{m|n} f(m) */
 void divisor_zeta() { _ZETA(_UP _OP(j, j - k, +)) }
 /* f -> h s.t. f(n) = sum_{m|n} h(m) */
 void divisor_mobius() { _ZETA(_DWN _OP(j, j - k, -)) }
 /* f -> g s.t. g(n) = sum_{n|m} f(m) */
 void multiple_zeta() { _ZETA(_DWN _OP(j - k, j, +)) }
 /* f -> h s.t. f(n) = sum_{n|m} h(m) */
 void multiple_mobius() { _ZETA(_UP _OP(j - k, j, -)) }
 /* f -> g s.t. g(n) = sum_{m|n} f(m), add(T& a, T b): a+=b */
 template <class F> void divisor_zeta(const F &add) { _ZETA(_UP _FUN(j, j - k, add)) }
 /* f -> h s.t. f(n) = sum_{m|n} h(m), sub(T& a, T b): a-=b */
 template <class F> void divisor_mobius(const F &sub) { _ZETA(_UP _FUN(j, j - k, sub)) }
 /* f -> g s.t. g(n) = sum_{n|m} f(m), add(T& a, T b): a+=b */
 template <class F> void multiple_zeta(const F &add) { _ZETA(_UP _FUN(j - k, j, add)) }
 /* f -> h s.t. f(n) = sum_{n|m} h(m), sub(T& a, T b): a-=b */
 template <class F> void multiple_mobius(const F &sub) { _ZETA(_UP _FUN(j - k, j, sub)) }
#undef _UP
#undef _DWN
#undef _OP
#undef _ZETA
 // f(p,e): multiplicative function of p^e
 template <typename F> void set_multiplicative(const F &f) {
  int k= 1;
  dat[0].second= 1;
  for (auto [p, e]: factors)
   for (int m= k, d= 1; d <= e; ++d)
    for (int i= 0; i < m;) dat[k++].second= dat[i++].second * f(p, d);
 }
 void set_totient() {
  int k= 1;
  dat[0].second= 1;
  for (auto [p, e]: factors) {
   uint64_t b= p - 1;
   for (int m= k; e--; b*= p)
    for (int i= 0; i < m;) dat[k++].second= dat[i++].second * b;
  }
 }
 void set_mobius() {
  set_multiplicative([](auto, auto e) { return e == 1 ? -1 : 0; });
 }
};
template <class mod_t> class FactorialPrecalculation {
 static_assert(is_modint_v<mod_t>);
 static inline std::vector<mod_t> iv, fct, fiv;
public:
 static void reset() { iv.clear(), fct.clear(), fiv.clear(); }
 static inline mod_t inv(int n) {
  assert(0 < n);
  if (int k= iv.size(); k <= n) {
   if (iv.resize(n + 1); !k) iv[1]= 1, k= 2;
   for (int mod= mod_t::mod(), q; k <= n; ++k) q= (mod + k - 1) / k, iv[k]= iv[k * q - mod] * q;
  }
  return iv[n];
 }
 static inline mod_t fact(int n) {
  assert(0 <= n);
  if (int k= fct.size(); k <= n) {
   if (fct.resize(n + 1); !k) fct[0]= 1, k= 1;
   for (; k <= n; ++k) fct[k]= fct[k - 1] * k;
  }
  return fct[n];
 }
 static inline mod_t finv(int n) {
  assert(0 <= n);
  if (int k= fiv.size(); k <= n) {
   if (fiv.resize(n + 1); !k) fiv[0]= 1, k= 1;
   for (; k <= n; ++k) fiv[k]= fiv[k - 1] * inv(k);
  }
  return fiv[n];
 }
 static inline mod_t nPr(int n, int r) { return r < 0 || n < r ? mod_t(0) : fact(n) * finv(n - r); }
 // [x^r] (1 + x)^n
 static inline mod_t nCr(int n, int r) { return r < 0 || n < r ? mod_t(0) : fact(n) * finv(n - r) * finv(r); }
 // [x^r] (1 - x)^{-n}
 static inline mod_t nHr(int n, int r) { return !r ? mod_t(1) : nCr(n + r - 1, r); }
};
using namespace std;
signed main() {
 cin.tie(0);
 ios::sync_with_stdio(0);
 using Mint= ModInt<int(1e9) + 7>;
 using F= FactorialPrecalculation<Mint>;
 int K;
 cin >> K;
 int tot= 0, g= 0;
 vector<int> C(K);
 for (int i= 0; i < K; ++i) cin >> C[i], tot+= C[i], g= gcd(g, C[i]);
 Mint ans= 0;
 ArrayOnDivisors<Mint> A(g);
 A.set_totient();
 for (auto [d, phi]: A) {
  Mint tmp= F::fact(tot / d);
  for (int i= 0; i < K; ++i) tmp*= F::finv(C[i] / d);
  tmp*= phi;
  ans+= tmp;
 }
 ans/= tot;
 cout << ans << '\n';
 return 0;
}
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