#include #include #include #include #define rep(i,a,b) for(int i=(a);i<(b);i++) #define rrep(i,a,b) for(int i=(b)-1;i>=(a);i--) #define all(x) begin(x),end(x) #define sz(x) (int)(x).size() using namespace std; // using namespace atcoder; using ll=long long; using ld=long double; using vll=vector; using vvll=vector; using vi=vector; using vvi=vector; using pll=pair; using pi=pair; // using mint=modint998244353; using mint=atcoder::modint1000000007; // using mint2=static_modint<2>; // using BoostPoint=boost::polygon::point_data; // using Voronoi=boost::polygon::voronoi_diagram; // using mint=LazyMontgomeryModInt<998244353>; using vm=vector; // using vvm=vector; #line 2 "math/rational.hpp" #include #include #include using namespace std; #line 2 "internal/internal-type-traits.hpp" #include using namespace std; namespace internal { template using is_broadly_integral = typename conditional_t || is_same_v || is_same_v, true_type, false_type>::type; template using is_broadly_signed = typename conditional_t || is_same_v, true_type, false_type>::type; template using is_broadly_unsigned = typename conditional_t || is_same_v, true_type, false_type>::type; #define ENABLE_VALUE(x) \ template \ constexpr bool x##_v = x::value; ENABLE_VALUE(is_broadly_integral); ENABLE_VALUE(is_broadly_signed); ENABLE_VALUE(is_broadly_unsigned); #undef ENABLE_VALUE #define ENABLE_HAS_TYPE(var) \ template \ struct has_##var : false_type {}; \ template \ struct has_##var> : true_type {}; \ template \ constexpr auto has_##var##_v = has_##var::value; #define ENABLE_HAS_VAR(var) \ template \ struct has_##var : false_type {}; \ template \ struct has_##var> : true_type {}; \ template \ constexpr auto has_##var##_v = has_##var::value; } // namespace internal #line 2 "math-fast/gcd.hpp" #include using namespace std; namespace BinaryGCDImpl { using u64 = unsigned long long; using i8 = char; u64 binary_gcd(u64 a, u64 b) { if (a == 0 || b == 0) return a + b; i8 n = __builtin_ctzll(a); i8 m = __builtin_ctzll(b); a >>= n; b >>= m; n = min(n, m); while (a != b) { u64 d = a - b; i8 s = __builtin_ctzll(d); bool f = a > b; b = f ? b : a; a = (f ? d : -d) >> s; } return a << n; } using u128 = __uint128_t; // a > 0 int ctz128(u128 a) { u64 lo = a & u64(-1); return lo ? __builtin_ctzll(lo) : 64 + __builtin_ctzll(a >> 64); } u128 binary_gcd128(u128 a, u128 b) { if (a == 0 || b == 0) return a + b; i8 n = ctz128(a); i8 m = ctz128(b); a >>= n; b >>= m; n = min(n, m); while (a != b) { u128 d = a - b; i8 s = ctz128(d); bool f = a > b; b = f ? b : a; a = (f ? d : -d) >> s; } return a << n; } } // namespace BinaryGCDImpl long long binary_gcd(long long a, long long b) { return BinaryGCDImpl::binary_gcd(abs(a), abs(b)); } __int128_t binary_gcd128(__int128_t a, __int128_t b) { if (a < 0) a = -a; if (b < 0) b = -b; return BinaryGCDImpl::binary_gcd128(a, b); } /** * @brief binary GCD */ #line 10 "math/rational.hpp" // T : 値, U : 比較用 template struct RationalBase { using R = RationalBase; using Key = T; T x, y; RationalBase() : x(0), y(1) {} template RationalBase(const T1& _x) : RationalBase(_x, T1{1}) {} template RationalBase(const pair& _p) : RationalBase(_p.first, _p.second) {} template RationalBase(const T1& _x, const T2& _y) : x(_x), y(_y) { assert(y != 0); if (y == -1) x = -x, y = -y; if (y != 1) { T g; if constexpr (internal::is_broadly_integral_v) { if constexpr (sizeof(T) == 16) { g = binary_gcd128(x, y); } else { g = binary_gcd(x, y); } } else { g = gcd(x, y); } if (g != 0) x /= g, y /= g; if (y < 0) x = -x, y = -y; } } // y = 0 の代入も認める static R raw(T _x, T _y) { R r; r.x = _x, r.y = _y; return r; } friend R operator+(const R& l, const R& r) { if (l.y == r.y) return R{l.x + r.x, l.y}; return R{l.x * r.y + l.y * r.x, l.y * r.y}; } friend R operator-(const R& l, const R& r) { if (l.y == r.y) return R{l.x - r.x, l.y}; return R{l.x * r.y - l.y * r.x, l.y * r.y}; } friend R operator*(const R& l, const R& r) { return R{l.x * r.x, l.y * r.y}; } friend R operator/(const R& l, const R& r) { return R{l.x * r.y, l.y * r.x}; } R& operator+=(const R& r) { return (*this) = (*this) + r; } R& operator-=(const R& r) { return (*this) = (*this) - r; } R& operator*=(const R& r) { return (*this) = (*this) * r; } R& operator/=(const R& r) { return (*this) = (*this) / r; } R operator-() const { return raw(-x, y); } R inverse() const { assert(x != 0); R r = raw(y, x); if (r.y < 0) r.x = -r.x, r.y = -r.y; return r; } R pow(long long p) const { R res{1}, base{*this}; while (p) { if (p & 1) res *= base; base *= base; p >>= 1; } return res; } friend bool operator==(const R& l, const R& r) { return l.x == r.x && l.y == r.y; }; friend bool operator!=(const R& l, const R& r) { return l.x != r.x || l.y != r.y; }; friend bool operator<(const R& l, const R& r) { return U{l.x} * r.y < U{l.y} * r.x; }; friend bool operator<=(const R& l, const R& r) { return l < r || l == r; } friend bool operator>(const R& l, const R& r) { return U{l.x} * r.y > U{l.y} * r.x; }; friend bool operator>=(const R& l, const R& r) { return l > r || l == r; } friend ostream& operator<<(ostream& os, const R& r) { os << r.x; if (r.x != 0 && r.y != 1) os << "/" << r.y; return os; } // T にキャストされるので T が bigint の場合は to_ll も要る T to_mint(T mod) const { assert(mod != 0); T a = y, b = mod, u = 1, v = 0, t; while (b > 0) { t = a / b; swap(a -= t * b, b); swap(u -= t * v, v); } return U((u % mod + mod) % mod) * x % mod; } }; using Rational = RationalBase; using Fraction = Rational; struct node{ Rational t; ll w; }; int main() { ios::sync_with_stdio(false); cin.tie(nullptr); //重み付き中央値という問題に帰着できます //再帰を使えばO(N)で解けます(線形選択アルゴリズムと大きく変わりません) int N; cin>>N; vll A(N); rep(i,0,N)cin>>A[i]; vectorv; ll W=0; rep(i,0,N){ ll b; cin>>b; if(A[i]==0)continue; ll w=abs(A[i]); v.push_back({Rational(b,A[i]),w}); W+=w; } ll K=(W+1)/2; auto lo=v.begin(),hi=v.end(); while(1){ auto mid=lo+(hi-lo)/2; nth_element(lo,mid,hi,[](const auto&a,const auto& b){return a.tt; //[lo,m1): t_i < p //[m1,m2): t_i = p //[m2,hi): t_i > p auto m1=partition(lo,hi,[&](const auto&a){return a.tw; for(auto it=m1;it!=m2;++it)E+=it->w; if(K<=L){ //左に再帰 hi=m1; }else if(K<=L+E){ //pが答え cout<<(mint(p.x)/mint(p.y)).val()<<'\n'; return 0; }else{ //右に再帰 K-=L+E; lo=m2; } } }