// #pragma GCC target ("avx") // #pragma GCC optimize("Ofast") #pragma GCC optimize("O3") #pragma GCC optimize("unroll-loops") #ifdef MARC_LOCAL #define _GLIBCXX_DEBUG #endif #ifdef ATCODER #include <atcoder/all> using namespace atcoder; #endif #include <bits/stdc++.h> using namespace std; //#define int long long using ll = long long; using vll = vector<ll>; using vvll = vector<vll>; using vvvll = vector<vvll>; using vvvvll = vector<vvvll>; using vi = vector<int>; using vvi = vector<vi>; using vvvi = vector<vvi>; using vvvvi = vector<vvvi>; using ld = long double; using vld = vector<ld>; using vvld = vector<vld>; using vd = vector<double>; using vc = vector<char>; using vvc = vector<vc>; using vs = vector<string>; using vb = vector<bool>; using vvb = vector<vb>; using vvvb = vector<vvb>; using pii = pair<int, int>; using pcc = pair<char, char>; using pll = pair<ll, ll>; using pli = pair<ll, int>; using pdd = pair<double, double>; using pldld = pair<ld,ld>; using vpii = vector<pii>; using vvpii = vector<vpii>; using vpll = vector<pll>; using vvpll = vector<vpll>; using vpldld = vector<pldld>; using ui = unsigned int; using ull = unsigned long long; using i128 = __int128; using f128 = __float128; template<class T> using pqg = priority_queue<T, vector<T>, greater<T>>; #define vec(type, name, ...) vector<type> name(__VA_ARGS__) // #define vv(type, name, h, ...) vector<vector<type> > name(h, vector<type>(__VA_ARGS__)) // #define vvv(type, name, h, w, ...) vector<vector<vector<type> > > name(h, vector<vector<type> >(w, vector<type>(__VA_ARGS__))) // #define vvvv(type, name, a, b, c, ...) vector<vector<vector<vector<type> > > > name(a, vector<vector<vector<type> > >(b, vector<vector<type> >(c, vector<type>(__VA_ARGS__)))) #define overload4(a,b,c,d,name,...) name #define rep1(n) for(ll i = 0; i < (ll)n; i++) #define rep2(i,n) for(ll i = 0; i < (ll)n; i++) #define rep3(i,a,b) for (ll i = a; i < (ll)b; i++) #define rep4(i,a,b,c) for (ll i = a; i < (ll)b; i += (ll)c) #define rep(...) overload4(__VA_ARGS__,rep4,rep3,rep2,rep1)(__VA_ARGS__) #define repback1(n) for (ll i = (ll)n-1; i >= 0; i--) #define repback2(i,n) for (ll i = (ll)n-1; i >= 0; i--) #define repback3(i,a,b) for (ll i = (ll)b-1; i >= (ll)a; i--) #define repback4(i,a,b,c) for (ll i = (ll)b-1; i >= (ll)a; i -= (ll)c) #define repback(...) overload4(__VA_ARGS__,repback4,repback3,repback2,repback1)(__VA_ARGS__) #define all(x) (x).begin(), (x).end() #define include(y, x, H, W) (0 <= (y) && (y) < (H) && 0 <= (x) && (x) < (W)) #define inrange(x, down, up) ((down) <= (x) && (x) <= (up)) #define square(x) (x) * (x) #define pb push_back #define eb emplace_back #define fir first #define sec second #define equals(a,b) (fabs((a) - (b)) < EPS) #define TIMER_START TIME_START = clock() #ifdef MARC_LOCAL // https://trap.jp/post/1224/ #define debug1(x) cout << "debug: " << (#x) << ": " << (x) << endl #define debug2(x, y) cout << "debug: " << (#x) << ": " << (x) << ", " << (#y) << ": " << (y) << endl #define debug3(x, y, z) cout << "debug: " << (#x) << ": " << (x) << ", " << (#y) << ": " << (y) << ", " << (#z) << ": " << (z) << endl #define debug4(x, y, z, w) cout << "debug: " << (#x) << ": " << (x) << ", " << (#y) << ": " << (y) << ", " << (#z) << ": " << (z) << ", " << (#w) << ": " << (w) << endl #define debug5(x, y, z, w, v) cout << "debug: " << (#x) << ": " << (x) << ", " << (#y) << ": " << (y) << ", " << (#z) << ": " << (z) << ", " << (#w) << ": " << (w) << ", " << (#v) << ": " << (v) << endl #define debug6(x, y, z, w, v, u) cout << "debug: " << (#x) << ": " << (x) << ", " << (#y) << ": " << (y) << ", " << (#z) << ": " << (z) << ", " << (#w) << ": " << (w) << ", " << (#v) << ": " << (v) << ", " << (#u) << ": " << (u) << endl #define overload6(a, b, c, d, e, f, g,...) g #define debug(...) overload6(__VA_ARGS__, debug6, debug5, debug4, debug3, debug2, debug1)(__VA_ARGS__) #define debuga cerr << "a" << endl #define debugnl cout << endl #define Case(i) cout << "Case #" << (i) << ": " #define TIMECHECK cerr << 1000.0 * static_cast<double>(clock() - TIME_START) / CLOCKS_PER_SEC << "ms" << endl #define LOCAL 1 #else #define debug1(x) void(0) #define debug2(x, y) void(0) #define debug3(x, y, z) void(0) #define debug4(x, y, z, w) void(0) #define debug5(x, y, z, w, v) void(0) #define debug6(x, y, z, w, v, u) void(0) #define debug(...) void(0) #define debuga void(0) #define debugnl void(0) #define Case(i) void(0) #define TIMECHECK void(0) #define LOCAL 0 #endif //mt19937_64 rng(0); mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count()); clock_t TIME_START; const long double pi = 3.1415926535897932; const long long INFL = 1000000000000000000ll; const long long INFLMAX = numeric_limits< long long >::max(); // 9223372036854775807 const int INF = 1000000000; const int INFMAX = numeric_limits< int >::max(); // 2147483647 const long double INFD = numeric_limits<ld>::infinity(); const long double EPS = 1e-9; const int mod1 = 1000000007; const int mod2 = 998244353; const vi dx1 = {1,0,-1,0}; const vi dy1 = {0,1,0,-1}; const vi dx2 = {0, 1, 1, 1, 0, -1, -1, -1, 0}; const vi dy2 = {1, 1, 0, -1, -1, -1, 0, 1, 1}; constexpr char nl = '\n'; constexpr char bl = ' '; std::ostream &operator<<(std::ostream &dest, __int128_t value) { std::ostream::sentry s(dest); if (s) {__uint128_t tmp = value < 0 ? -value : value; char buffer[128]; char *d = std::end(buffer); do {--d;*d = "0123456789"[tmp % 10];tmp /= 10;} while (tmp != 0);if (value < 0) {--d;*d = '-';}int len = std::end(buffer) - d;if (dest.rdbuf()->sputn(d, len) != len) {dest.setstate(std::ios_base::badbit);}}return dest; } __int128 parse(string &s) { __int128 ret = 0; for (int i = 0; i < (int)s.length(); i++) if ('0' <= s[i] && s[i] <= '9') ret = 10 * ret + s[i] - '0'; return ret; } // for __int128 (https://kenkoooo.hatenablog.com/entry/2016/11/30/163533) template<typename T> ostream& operator << (ostream& os, vector<T>& vec) { os << "["; for (int i = 0; i<(int)vec.size(); i++) { os << vec[i] << (i + 1 == (int)vec.size() ? "" : ", "); } os << "]"; return os; } /// vector 出力 template<typename T, typename U> ostream& operator << (ostream& os, pair<T, U>& pair_var) { os << "(" << pair_var.first << ", " << pair_var.second << ")"; return os; } // pair 出力 template<typename T, typename U> ostream& operator << (ostream& os, map<T, U>& map_var) { os << "{"; for (auto itr = map_var.begin(); itr != map_var.end(); itr++) { os << "(" << itr->first << ", " << itr->second << ")"; itr++; if(itr != map_var.end()) os << ", "; itr--; } os << "}"; return os; } // map出力 template<typename T> ostream& operator << (ostream& os, set<T>& set_var) { os << "{"; for (auto itr = set_var.begin(); itr != set_var.end(); itr++) { os << *itr; ++itr; if(itr != set_var.end()) os << ", "; itr--; } os << "}"; return os; } /// set 出力 int popcnt(unsigned long long a){ return __builtin_popcountll(a); } // ll は 64bit対応! int MSB1(unsigned long long x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); } // MSB(1), 0-indexed ( (0, 1, 2, 3, 4) -> (-1, 0, 1, 1, 2) ) int LSB1(unsigned long long x) { return (x == 0 ? -1 : __builtin_ctzll(x)); } // LSB(1), 0-indexed ( (0, 1, 2, 3, 4) -> (-1, 0, 1, 0, 2) ) long long pow2(int n) { return 1LL << n; } long long maskbit(int n) { return (1LL << n) - 1; } bool bit_is1(long long x, int i) { return ((x>>i) & 1); } string charrep(int n, char c) { return std::string(n, c); } template<class T>void UNIQUE(T& A) {sort(all(A)); A.erase(unique(all(A)), A.end());} template<class T>bool chmax(T& a, const T& b) { if (a < b) { a = b; return 1; } return 0; } template<class T>bool chmin(T& a, const T& b) { if (b < a) { a = b; return 1; } return 0; } template<class T, class U> bool chmin(T& a, const U& b){ return chmin(a, (T)b); } template<class T, class U> bool chmax(T& a, const U& b){ return chmax(a, (T)b); } void YESNO(bool b) {if(b){cout<<"YES"<<'\n';} else{cout<<"NO"<<'\n';}} void YES() {YESNO(true);} void NO() {YESNO(false);} void yesno(bool b) {if(b){cout<<"yes"<<'\n';} else{cout<<"no"<<'\n';}} void yes() {yesno(true);} void no() {yesno(false);} void POSIMPOS(bool b) {if(b){cout<<"POSSIBLE"<<'\n';} else{cout<<"IMPOSSIBLE"<<'\n';}} void PosImpos(bool b) {if(b){cout<<"Possible"<<'\n';} else{cout<<"Impossible"<<'\n';}} void posimpos(bool b) {if(b){cout<<"possible"<<'\n';} else{cout<<"impossible"<<'\n';}} void FIRSEC(bool b) {if(b){cout<<"FIRST"<<'\n';} else{cout<<"SECOND"<<'\n';}} void firsec(bool b) {if(b){cout<<"first"<<'\n';} else{cout<<"second"<<'\n';}} void FirSec(bool b) {if(b){cout<<"First"<<'\n';} else{cout<<"Second"<<'\n';}} void AliBob(bool b) {if(b){cout<<"Alice"<<'\n';} else{cout<<"Bob"<<'\n';}} void TakAok(bool b) {if(b){cout<<"Takahashi"<<'\n';} else{cout<<"Aoki"<<'\n';}} int GetTime() {return 1000.0*static_cast<double>(clock() - TIME_START) / CLOCKS_PER_SEC;} ll myRand(ll B) {return (unsigned long long)rng() % B;} template<typename T> void print(const T& x, const char endch = '\n') { cout << x << endch; } template<class T> T ceil_div(T x, T y) { assert(y); return (x > 0 ? (x + y - 1) / y : x / y); } template<class T> T floor_div(T x, T y) { assert(y); return (x > 0 ? x / y : (x - y + 1) / y); } template<class T> pair<T, T> divmod(T x, T y) { T q = floor_div(x, y); return {q, x - q * y}; } /// (q, r) s.t. x = q*y + r ll GCD(ll a, ll b) { if(a < b) swap(a, b); if(b == 0) return a; if(a%b == 0) return b; else return GCD(b, a%b); } ll LCM(ll a, ll b) { assert(GCD(a,b) != 0); return a / GCD(a, b) * b; } ll MOD(ll &x, const ll P) { ll ret = x%P; if(ret < 0) ret += P; return x = ret; } /// x % P を非負整数に直す ll mpow(ll x, ll n, const ll mod) { x %= mod; ll ret = 1; while(n > 0) { if(n & 1) ret = ret * x % mod; x = x * x % mod; n >>= 1; } return ret; } /// x^n % mod を計算 ll lpow(ll x, ll n) { ll ret = 1; while(n > 0){ if(n & 1) ret = ret * x; x = x * x; n >>= 1; } return ret; } /// x^nを計算 string toBinary(ll n) { if(n == 0) return "0"; assert(n > 0); string ret; while (n != 0){ ret += ( (n & 1) == 1 ? '1' : '0' ); n >>= 1; } reverse(ret.begin(), ret.end()); return ret; } /// 10進数(long long) -> 2進数(string)への変換 ll toDecimal(string S) { ll ret = 0; for(int i = 0; i < (int)S.size(); i++){ ret *= 2LL; if(S[i] == '1') ret += 1; } return ret; } /// 2進数(string) → 10進数(long long)への変換 int ceil_pow2(ll n) { int x = 0; while ((1ll << x) < n) x++; return x;} /// return minimum non-negative `x` s.t. `n <= 2**x` int floor_pow2(ll n) { int x = 0; while ((1ll << (x+1)) <= n) x++; return x;} /// return maximum non-negative `x` s.t. `n >= 2**x` #include <unistd.h> // yosupo-san arigatou namespace yosupo_IO { template <class T> using is_signed_int128 = typename std::conditional<is_same<T, __int128_t>::value || is_same<T, __int128>::value, true_type, false_type>::type; template <class T> using is_unsigned_int128 = typename std::conditional<is_same<T, __uint128_t>::value || is_same<T, unsigned __int128>::value, true_type, false_type>::type; template <class T> using make_unsigned_int128 = typename std::conditional<is_same<T, __int128_t>::value, __uint128_t, unsigned __int128>; template <class T> using is_integral = typename std::conditional<std::is_integral<T>::value || is_signed_int128<T>::value || is_unsigned_int128<T>::value, true_type, false_type>::type; template <class T> using is_signed_int = typename std::conditional<(is_integral<T>::value && std::is_signed<T>::value) || is_signed_int128<T>::value, true_type, false_type>::type; template <class T> using is_unsigned_int = typename std::conditional<(is_integral<T>::value && std::is_unsigned<T>::value) || is_unsigned_int128<T>::value, true_type, false_type>::type; template <class T> using to_unsigned = typename std::conditional< is_signed_int128<T>::value, make_unsigned_int128<T>, typename std::conditional<std::is_signed<T>::value, std::make_unsigned<T>, std::common_type<T>>::type>::type; template <class T> using is_integral_t = enable_if_t<is_integral<T>::value>; template <class T> using is_signed_int_t = enable_if_t<is_signed_int<T>::value>; template <class T> using is_unsigned_int_t = enable_if_t<is_unsigned_int<T>::value>; namespace detail { template <typename T, decltype(&T::is_modint) = &T::is_modint> std::true_type check_value(int); template <typename T> std::false_type check_value(long); } // namespace detail template <typename T> struct is_modint : decltype(detail::check_value<T>(0)) {}; template <typename T> using is_modint_t = enable_if_t<is_modint<T>::value>; template <class T> using to_unsigned_t = typename to_unsigned<T>::type; struct Scanner { public: Scanner(const Scanner &) = delete; Scanner &operator=(const Scanner &) = delete; Scanner(FILE *fp) : fd(fileno(fp)) { line[0] = 127; } void read() {} template <class H, class... T> void read(H &h, T &... t) { bool f = read_single(h); assert(f); read(t...); } int read_unsafe() { return 0; } template <class H, class... T> int read_unsafe(H &h, T &... t) { bool f = read_single(h); if (!f) return 0; return 1 + read_unsafe(t...); } int close() { return ::close(fd); } private: static constexpr int SIZE = 1 << 15; int fd = -1; array<char, SIZE + 1> line; int st = 0, ed = 0; bool eof = false; bool read_single(string &ref) { if (!skip_space()) return false; ref = ""; while (true) { char c = top(); if (c <= ' ') break; ref += c; st++; } return true; } bool read_single(double &ref) { string s; if (!read_single(s)) return false; ref = std::stod(s); return true; } template <class T, enable_if_t<is_same<T, char>::value> * = nullptr> bool read_single(T &ref) { if (!skip_space<50>()) return false; ref = top(); st++; return true; } template <class T, is_signed_int_t<T> * = nullptr, enable_if_t<!is_same<T, char>::value> * = nullptr> bool read_single(T &sref) { using U = to_unsigned_t<T>; if (!skip_space<50>()) return false; bool neg = false; if (line[st] == '-') { neg = true; st++; } U ref = 0; do { ref = 10 * ref + (line[st++] & 0x0f); } while (line[st] >= '0'); sref = neg ? -ref : ref; return true; } template <class U, is_unsigned_int_t<U> * = nullptr, enable_if_t<!is_same<U, char>::value> * = nullptr> bool read_single(U &ref) { if (!skip_space<50>()) return false; ref = 0; do { ref = 10 * ref + (line[st++] & 0x0f); } while (line[st] >= '0'); return true; } bool reread() { if (ed - st >= 50) return true; if (st > SIZE / 2) { std::memmove(line.data(), line.data() + st, ed - st); ed -= st; st = 0; } if (eof) return false; auto u = ::read(fd, line.data() + ed, SIZE - ed); if (u == 0) { eof = true; line[ed] = '\0'; u = 1; } ed += int(u); line[ed] = char(127); return true; } char top() { if (st == ed) { bool f = reread(); assert(f); } return line[st]; } template <int TOKEN_LEN = 0> bool skip_space() { while (true) { while (line[st] <= ' ') st++; if (ed - st > TOKEN_LEN) return true; if (st > ed) st = ed; for (auto i = st; i < ed; i++) { if (line[i] <= ' ') return true; } if (!reread()) return false; } } }; struct Printer { public: template <char sep = ' ', bool F = false> void write() {} template <char sep = ' ', bool F = false, class H, class... T> void write(const H &h, const T &... t) { if (F) write_single(sep); write_single(h); write<true>(t...); } template <char sep = ' ', class... T> void writeln(const T &... t) { write<sep>(t...); write_single('\n'); } Printer(FILE *_fp) : fd(fileno(_fp)) {} ~Printer() { flush(); } int close() { flush(); return ::close(fd); } void flush() { if (pos) { auto res = ::write(fd, line.data(), pos); assert(res != -1); pos = 0; } } private: static array<array<char, 2>, 100> small; static array<unsigned long long, 20> tens; static constexpr size_t SIZE = 1 << 15; int fd; array<char, SIZE> line; size_t pos = 0; std::stringstream ss; template <class T, enable_if_t<is_same<char, T>::value> * = nullptr> void write_single(const T &val) { if (pos == SIZE) flush(); line[pos++] = val; } template <class T, is_signed_int_t<T> * = nullptr, enable_if_t<!is_same<char, T>::value> * = nullptr> void write_single(const T &val) { using U = to_unsigned_t<T>; if (val == 0) { write_single('0'); return; } if (pos > SIZE - 50) flush(); U uval = val; if (val < 0) { write_single('-'); uval = -uval; } write_unsigned(uval); } template <class T, is_modint_t<T> * = nullptr> void write_single(const T &val) { write_single(val.val); } static int bsr(unsigned int n) { return 8 * (int)sizeof(unsigned int) - 1 - __builtin_clz(n); } static int bsr(unsigned long n) { return 8 * (int)sizeof(unsigned long) - 1 - __builtin_clzl(n); } static int bsr(unsigned long long n) { return 8 * (int)sizeof(unsigned long long) - 1 - __builtin_clzll(n); } template <class U, is_unsigned_int_t<U> * = nullptr> void write_single(U uval) { if (uval == 0) { write_single('0'); return; } if (pos > SIZE - 50) flush(); write_unsigned(uval); } template <class U, is_unsigned_int_t<U> * = nullptr> static int calc_len(U x) { int i = (bsr(1ULL * x) * 3 + 3) / 10; if (x < tens[i]) return i; else return i + 1; } template <class U, is_unsigned_int_t<U> * = nullptr, enable_if_t<2 >= sizeof(U)> * = nullptr> void write_unsigned(U uval) { size_t len = calc_len(uval); pos += len; char *ptr = line.data() + pos; while (uval >= 100) { ptr -= 2; memcpy(ptr, small[uval % 100].data(), 2); uval /= 100; } if (uval >= 10) { memcpy(ptr - 2, small[uval].data(), 2); } else { *(ptr - 1) = char('0' + uval); } } template <class U, is_unsigned_int_t<U> * = nullptr, enable_if_t<4 == sizeof(U)> * = nullptr> void write_unsigned(U uval) { array<char, 8> buf; memcpy(buf.data() + 6, small[uval % 100].data(), 2); memcpy(buf.data() + 4, small[uval / 100 % 100].data(), 2); memcpy(buf.data() + 2, small[uval / 10000 % 100].data(), 2); memcpy(buf.data() + 0, small[uval / 1000000 % 100].data(), 2); if (uval >= 100000000) { if (uval >= 1000000000) { memcpy(line.data() + pos, small[uval / 100000000 % 100].data(), 2); pos += 2; } else { line[pos] = char('0' + uval / 100000000); pos++; } memcpy(line.data() + pos, buf.data(), 8); pos += 8; } else { size_t len = calc_len(uval); memcpy(line.data() + pos, buf.data() + (8 - len), len); pos += len; } } template <class U, is_unsigned_int_t<U> * = nullptr, enable_if_t<8 == sizeof(U)> * = nullptr> void write_unsigned(U uval) { size_t len = calc_len(uval); pos += len; char *ptr = line.data() + pos; while (uval >= 100) { ptr -= 2; memcpy(ptr, small[uval % 100].data(), 2); uval /= 100; } if (uval >= 10) { memcpy(ptr - 2, small[uval].data(), 2); } else { *(ptr - 1) = char('0' + uval); } } template <class U, enable_if_t<is_unsigned_int128<U>::value> * = nullptr> void write_unsigned(U uval) { static array<char, 50> buf; size_t len = 0; while (uval > 0) { buf[len++] = char((uval % 10) + '0'); uval /= 10; } std::reverse(buf.begin(), buf.begin() + len); memcpy(line.data() + pos, buf.data(), len); pos += len; } void write_single(const std::string &s) { for (char c: s) write_single(c); } void write_single(const char *s) { size_t len = strlen(s); for (size_t i = 0; i < len; i++) write_single(s[i]); } template <class T> void write_single(const std::vector<T> &val) { auto n = val.size(); for (size_t i = 0; i < n; i++) { if (i) write_single(' '); write_single(val[i]); } } }; array<array<char, 2>, 100> Printer::small = [] { array<array<char, 2>, 100> table; for (int i = 0; i <= 99; i++) { table[i][1] = char('0' + (i % 10)); table[i][0] = char('0' + (i / 10 % 10)); } return table; }(); array<ull, 20> Printer::tens = [] { array<ull, 20> table; for (int i = 0; i < 20; i++) { table[i] = 1; for (int j = 0; j < i; j++) { table[i] *= 10; } } return table; }(); } // namespace yosupo_IO using namespace yosupo_IO; Scanner scanner = Scanner(stdin); Printer printer = Printer(stdout); // ############################ // # # // # C O D E S T A R T # // # # // ############################ /// 有理数型 (x/y) // 分母分子が longlong 内に収まっても、比較の際の乗算でオーバーフローする可能性があることに注意 -> T = i128を使う template< class T = long long> class Fraction{ public: T x,y; /// 約分 void reduc(){ int minus = 1; T absx = x; T absy = y; if(x < 0) minus *= -1, absx *= -1; if(y < 0) minus *= -1, absy *= -1; T g = gcd(absx, absy); x = minus * absx / g; y = absy / g; } Fraction(T x = 0, T y = 1): x(x), y(y) {reduc();}; // 比較の際の乗算でオーバーフローすることがあることに注意 bool operator<(const Fraction& right) const {return x*right.y < y*right.x;} bool operator<=(const Fraction& right) const {return x*right.y <= y*right.x;} bool operator>(const Fraction& right) const {return x*right.y > y*right.x;} bool operator>=(const Fraction& right) const {return x*right.y >= y*right.x;} bool operator==(const Fraction& right) const {return x == right.x && y == right.y;} Fraction operator-() const {return Fraction(-x, y);} Fraction& operator+=(const Fraction& v){ x = x*v.y + y*v.x; y *= v.y; reduc(); return *this; } Fraction operator+(const Fraction& v) const {return Fraction(*this) += v;} Fraction& operator-=(const Fraction& v){ x = x*v.y - y*v.x; y *= v.y; reduc(); return *this; } Fraction operator-(const Fraction& v) const {return Fraction(*this) -= v;} Fraction& operator*=(const Fraction& v){ x *= v.x; y *= v.y; reduc(); return *this; } Fraction operator*(const Fraction& v) const {return Fraction(*this) *= v;} Fraction& operator/=(const Fraction& v){ x *= v.y; y *= v.x; reduc(); return *this; } Fraction operator/(const Fraction& v) const {return Fraction(*this) /= v;} Fraction inv() const {return Fraction(y,x);} Fraction pow(long long t) const { if(t < 0) return inv().pow(-t); Fraction a(1, 1), d = *this; while(t){ d *= d; if(t & 1) a *= d; t >>= 1; } return a; } friend ostream& operator << (ostream& os, const Fraction& v){ return os << v.x << '/' << v.y;} private: T gcd(T a, T b){ if(a < b) swap(a, b); if(b == 0) return a; if(a%b == 0) return b; else return gcd(b, a%b); } }; #include<boost/multiprecision/cpp_int.hpp> using Fractionll = Fraction<boost::multiprecision::int256_t>; using namespace boost::multiprecision; void YesNo(bool b) {if(b){printer.writeln("Yes");} else{printer.writeln("No");}} // https://www.mynote-jp.com/entry/Circle-Defined-by-Three-Points void solve() { int Q; scanner.read(Q); vll X(3); vll Y(3); rep(i,3) scanner.read(X[i], Y[i]); ll a = X[0] - X[1]; ll b = Y[0] - Y[1]; ll c = X[1] - X[2]; ll d = Y[1] - Y[2]; ll bunbo = 2 * (a * d - b * c); debug(bunbo); if(bunbo == 0) { vpll XY(3); rep(i,3) XY[i] = {X[i],Y[i]}; sort(all(XY)); ll cx = XY[1].first; ll cy = XY[1].second; ll r2 = square(X[0] - cx) + square(Y[0] - cy); while(Q--) { ll x,y; scanner.read(x, y); ll dist = square(x - cx) + square(y - cy); YesNo(dist <= r2); } return; } ll e = square(X[0]) + square(Y[0]) - (square(X[1]) + square(Y[1])); ll f = square(X[1]) + square(Y[1]) - (square(X[2]) + square(Y[2])); Fractionll cx(d*e - b*f, bunbo); Fractionll cy(-c*e + a*f, bunbo); Fractionll r2 = square(Fractionll(X[0],1) - cx) + square(Fractionll(Y[0],1) - cy); debug(cx,cy,r2); while(Q--) { ll x,y; scanner.read(x, y); Fractionll dist = square(Fractionll(x,1) - cx) + square(Fractionll(y,1) - cy); cpp_int p = dist.x * r2.y; cpp_int q = dist.y * r2.x; //YesNo(dist <= r2); YesNo(p <= q); } } signed main() { cin.tie(0); ios_base::sync_with_stdio(false); TIMER_START; //cout << fixed << setprecision(15); int tt = 1; //cin >> tt; while(tt--){ solve(); } TIMECHECK; return 0; }