//#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,avx2,avx512f") #pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx") #pragma GCC optimize("O3") #pragma GCC optimize("unroll-loops") #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #ifdef DEBUG #include "./CompetitiveProgrammingCpp/debug.hpp" #include "./CompetitiveProgrammingCpp/Timer.hpp" #include "./CompetitiveProgrammingCpp/sample.hpp" #else #define dump(...) #endif /* macro */ #define FOR(i, b, e) for(ll i = (ll)(b); i < (ll)(e); ++i) #define RFOR(i, b, e) for(ll i = (ll)((e)-1); i >= (ll)(b); --i) #define REP(i, n) FOR(i, 0, (n)) #define RREP(i, n) RFOR(i, 0, (n)) #define REPC(x,c) for(const auto& x:(c)) #define REPI2(it,b,e) for(auto it = (b); it != (e); ++it) #define REPI(it,c) REPI2(it, (c).begin(), (c).end()) #define RREPI(it,c) REPI2(it, (c).rbegin(), (c).rend()) #define REPI_ERACE2(it, b, e) for(auto it = (b); it != (e);) #define REPI_ERACE(it, c) REPI_ERACE2(it, (c).begin(), (c).end()) #define ALL(x) (x).begin(),(x).end() #define cauto const auto& /* macro func */ template inline auto sort(T& t) { std::sort(ALL(t)); } template inline auto rsort(T& t) { std::sort((t).rbegin(), (t).rend()); } template inline auto unique(T& t) { (t).erase(unique((t).begin(), (t).end()), (t).end()); } template inline auto chmax(T& t, const S& s) { if(s > t) { t = s; return true; } return false; } template inline auto chmin(T& t, const S& s) { if(s < t) { t = s; return true; } return false; } inline auto BR() { std::cout << "\n"; } /* type define */ using ll = long long; using VS = std::vector; using VL = std::vector; using VVL = std::vector; using VVVL = std::vector; using VVVVL = std::vector; using VVVVVL = std::vector; using VD = std::vector; template using V = std::vector; template using P = std::pair; using PAIR = P; /* using std */ using std::cout; constexpr char endl = '\n'; using std::cin; using std::pair; using std::string; using std::stack; using std::queue; using std::deque; using std::vector; using std::list; using std::map; using std::unordered_map; using std::multimap; using std::unordered_multimap; using std::set; using std::unordered_set; using std::unordered_multiset; using std::multiset; using std::bitset; using std::priority_queue; /* Initial processing */ struct Preprocessing { Preprocessing() { std::cin.tie(0); std::ios::sync_with_stdio(0); }; }_Preprocessing; /* Remove the source of the bug */ auto pow(signed, signed) { assert(false); } /* define hash */ namespace std { template <> class hash> { public: size_t operator()(const std::pair& x) const { return hash()(1000000000 * x.first + x.second); } }; } /* input */ template std::istream& operator >> (std::istream& is, vector& vec) { for(T& x : vec) is >> x; return is; } /* constant value */ constexpr ll MOD = 1000000007; // constexpr ll MOD = 998244353; //============================================================================================= class EuclideanAlgorithm { using T = long long; const T m_a; const T m_b; const T m_mx; // 大きすぎるとオーバーフローしてしまう T m_gcd; T m_x; T m_y; auto excludedEuclidAlgorithm(T a, T b) -> std::tuple { if(a < 0) { auto [g, x, y] = excludedEuclidAlgorithm(-a, -b); return {g,-x,-y}; } if(b == 0) { return {a, 1, 0}; } auto [g, y, x] = excludedEuclidAlgorithm(b, a % b); y -= a / b * x; return {g, x, y}; } auto kRange(T x, T b, T l) const -> std::tuple { // x + b * k >= l を満たす k の範囲を求める T xd = (l - x); if(b == 0 && x >= l) { return {-m_mx,m_mx}; } if(b == 0 && x < l) { return {m_mx,-m_mx}; } if(b > 0 && xd < 0) { return {xd / b,m_mx}; } if(b > 0 && xd >= 0) { return {(xd + b - 1) / b,m_mx}; } if(b < 0 && xd < 0) { return {-m_mx,(-xd) / (-b)}; } if(b < 0 && xd >= 0) { return {-m_mx,-(xd - b - 1) / (-b)}; } return {m_mx,-m_mx}; } public: auto debug()const { std::cout << m_a << " * " << m_x << " + " << m_b << " * " << m_y << " = " << m_gcd << std::endl; std::cout << m_a * m_x + m_b * m_y << " = " << m_gcd << std::endl; } EuclideanAlgorithm(T a, T b, T mx = 1e9) :m_a(a), m_b(b), m_mx(mx) { if(a == 0 && b == 0) { throw std::runtime_error(""); } auto [g, x, y] = excludedEuclidAlgorithm(a, b); m_gcd = g; m_x = x; m_y = y; } auto gcd() const { return m_gcd; } auto get(T x, T y) const { return m_a * x + m_b * y; } auto get(T k) const ->std::tuple { if(m_b == 0) { return {m_x,m_y - k}; } if(m_a == 0) { return {m_x + k,m_y}; } return {m_x + m_b * k, m_y - m_a * k}; } auto getMinX(T x_l = 0)const -> std::tuple { return kRange(m_x, m_b, x_l); } auto getMinY(T y_l = 0)const -> std::tuple { return kRange(m_y, -1 * m_a, y_l); } auto getMin(T x_l = 0, T y_l = 0)const -> std::tuple { auto [xl, xr] = getMinX(x_l); auto [yl, yr] = getMinY(y_l); return {std::max(xl,yl),std::min(xr,yr)}; } }; using D = PAIR; auto operator<(const D& a, const D& b) { ll l = a.first * b.second; ll r = a.second * b.first; return l < r; } auto g(const D& d) { ll g = std::gcd(d.first, d.second); return D{d.first / g,d.second / g}; } auto solve(ll p, ll q) { auto pq = EuclideanAlgorithm(-p, q); auto [rk, _] = pq.getMin(1, 1); auto [rx, ry] = pq.get(rk); auto rg = pq.gcd(); auto qp = EuclideanAlgorithm(-q, p); auto [lk, __] = qp.getMin(1, 1); auto [lx, ly] = qp.get(lk); auto lg = qp.gcd(); ll ans = rx / rg + ry / rg + lx / lg + ly / lg; return ans; } auto solve_c(ll p, ll q) { D mx = {0,1}; D mn = {1,1}; FOR(i, 1, q) REP(j, i) { if(D{j, i} < D{p,q}) { if(mx < D{j,i}) { mx = D{j,i}; } } } FOR(i, 1, q) REP(j, i + 1) if(D{p,q} < D{j, i}) { chmin(mn, D{j,i}); } mn = g(mn); mx = g(mx); dump(mn, mx); return mx.first + mx.second + mn.second + mn.first; } signed main() { /**/ ll p, q; cin >> p >> q; auto ans = solve(p, q); cout << ans << endl; //cout << "-- cor --" << endl; //auto ans_c = solve_c(p, q); //cout << ans_c << endl; /*/ auto tm = Timer::SimpleTimer(); auto gen = Sample::SampleGenerator(); REP(_, 100) { auto [p] = gen.generate(PAIR{1,9}); auto [q] = gen.generate(PAIR{p + 1,10}); auto g = std::gcd(p, q); p /= g; q /= g; auto ans = solve(p, q); auto ans_c = solve_c(p, q); if(ans != ans_c) { cout << p << " " << q << endl; dump(ans, ans_c); return 0; } } tm.print(); /**/ }