//#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; //============================================================================================= long long extGCD(long long a, long long b, long long& x, long long& y) { if(b == 0) { x = 1; y = 0; return a; } long long d = extGCD(b, a % b, y, x); y -= a / b * x; return d; } 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) { D mn, mx; { ll x, y; extGCD(q, p, x, y); y = -y; ll n1 = (x > 0) ? 0 : (std::abs(x) + p) / p; ll n2 = (y > 0) ? 0 : (std::abs(y) + q) / q; ll need = std::max(n1, n2); y += q * need; mn.first = p * y + 1; mn.second = q * y; mn = g(mn); } { ll x, y; extGCD(p, q, x, y); y = -y; ll d = (q - x) / q; x += q * d; mx.first = p * x - 1; mx.second = q * x; mx = g(mx); } dump(mn, mx); ll ans = mn.first + mn.second + mx.first + mx.second; 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(); /**/ }