#include using namespace std; using ll = long long; using ld = long double; // -------------------------------------------------------- #define FOR(i,l,r) for (ll i = (l); i < (r); ++i) #define RFOR(i,l,r) for (ll i = (r)-1; (l) <= i; --i) #define REP(i,n) FOR(i,0,n) #define RREP(i,n) RFOR(i,0,n) #define ALL(c) (c).begin(), (c).end() #define RALL(c) (c).rbegin(), (c).rend() #define SORT(c) sort(ALL(c)) #define RSORT(c) sort(RALL(c)) #define MIN(c) *min_element(ALL(c)) #define MAX(c) *max_element(ALL(c)) #define COUNT(c,v) count(ALL(c),(v)) #define SZ(c) ((ll)(c).size()) #define BIT(b,i) (((b)>>(i)) & 1) #define PCNT(b) __builtin_popcountll(b) #define P0(i) (((i) & 1) == 0) #define P1(i) (((i) & 1) == 1) #define LB(c,v) distance((c).begin(), lower_bound(ALL(c), (v))) #define UB(c,v) distance((c).begin(), upper_bound(ALL(c), (v))) #define UQ(c) SORT(c), (c).erase(unique(ALL(c)), (c).end()) #define elif else if #ifdef _LOCAL #define debug_bar cerr << "--------------------\n"; #define debug(x) cerr << "l." << __LINE__ << " : " << #x << " = " << (x) << '\n' #define debug_pair(x) cerr << "l." << __LINE__ << " : " << #x << " = (" << x.first << "," << x.second << ")\n"; template void debug_line(const vector& ans, int l, int r, int L = 0) { cerr << "l." << L << " :"; for (int i = l; i < r; i++) { cerr << ' ' << ans[i]; } cerr << '\n'; } #else #define cerr if (false) cerr #define debug_bar #define debug(x) #define debug_pair(x) template void debug_line([[maybe_unused]] const vector& ans, [[maybe_unused]] int l, [[maybe_unused]] int r, [[maybe_unused]] int L = 0) {} #endif template void input(T&... a) { (cin >> ... >> a); } void print() { cout << '\n'; } template void print(const T& a) { cout << a << '\n'; } template void print(const T& a, const Ts&... b) { cout << a; (cout << ... << (cout << ' ', b)); cout << '\n'; } template void cout_line(const vector& ans, int l, int r) { for (int i = l; i < r; i++) { if (i != l) { cout << ' '; } cout << ans[i]; } cout << '\n'; } template bool chmin(T& a, const T b) { if (b < a) { a = b; return 1; } return 0; } template bool chmax(T& a, const T b) { if (a < b) { a = b; return 1; } return 0; } template T SUM(const vector& A) { return accumulate(ALL(A), T(0)); } template vector cumsum(const vector& A, bool offset = true) { int N = A.size(); vector S(N+1, 0); for (int i = 0; i < N; i++) { S[i+1] = S[i] + A[i]; } if (not offset) { S.erase(S.begin()); } return S; } ll mod(ll x, ll m) { assert(m != 0); return (x % m + m) % m; } ll ceil(ll a, ll b) { if (b < 0) { return ceil(-a, -b); } assert(b > 0); return (a < 0 ? a / b : (a + b - 1) / b); } ll floor(ll a, ll b) { if (b < 0) { return floor(-a, -b); } assert(b > 0); return (a > 0 ? a / b : (a - b + 1) / b); } ll powint(ll x, ll n) { assert(n >= 0); if (n == 0) { return 1; }; ll res = powint(x, n>>1); res *= res; if (n & 1) { res *= x; } return res; } pair divmod(ll a, ll b) { assert(b != 0); ll q = floor(a, b); return make_pair(q, a - q * b); } ll bitlen(ll b) { if (b <= 0) { return 0; } return (64LL - __builtin_clzll(b)); } ll digit_len(ll n) { assert(n >= 0); if (n == 0) { return 1; } ll sum = 0; while (n > 0) { sum++; n /= 10; } return sum; } ll digit_sum(ll n) { assert(n >= 0); ll sum = 0; while (n > 0) { sum += n % 10; n /= 10; } return sum; } ll digit_prod(ll n) { assert(n >= 0); if (n == 0) { return 0; } ll prod = 1; while (n > 0) { prod *= n % 10; n /= 10; } return prod; } ll xor_sum(ll x) { assert(0 <= x); switch (x % 4) { case 0: return x; case 1: return 1; case 2: return x ^ 1; case 3: return 0; } assert(false); } string toupper(const string& S) { string T(S); for (int i = 0; i < (int)T.size(); i++) { T[i] = toupper(T[i]); } return T; } string tolower(const string& S) { string T(S); for (int i = 0; i < (int)T.size(); i++) { T[i] = tolower(T[i]); } return T; } int a2i(const char& c) { assert(islower(c)); return (c - 'a'); } int A2i(const char& c) { assert(isupper(c)); return (c - 'A'); } int d2i(const char& d) { assert(isdigit(d)); return (d - '0'); } char i2a(const int& i) { assert(0 <= i && i < 26); return ('a' + i); } char i2A(const int& i) { assert(0 <= i && i < 26); return ('A' + i); } char i2d(const int& i) { assert(0 <= i && i <= 9); return ('0' + i); } using P = pair; using VP = vector

; using VVP = vector; using VS = vector; using VVS = vector; using VI = vector; using VVI = vector; using VVVI = vector; using VLL = vector; using VVLL = vector; using VVVLL = vector; using VB = vector; using VVB = vector; using VVVB = vector; using VD = vector; using VVD = vector; using VVVD = vector; using VLD = vector; using VVLD = vector; using VVVLD = vector; const ld EPS = 1e-10; const ld PI = acosl(-1.0); constexpr ll MOD = 1000000007; // constexpr ll MOD = 998244353; constexpr int inf = (1 << 30) - 1; // 1073741824 - 1 constexpr ll INF = (1LL << 62) - 1; // 4611686018427387904 - 1 // -------------------------------------------------------- // #include // using namespace atcoder; // References: // // // 線形ディオファントス方程式 // x + by = c の整数解の一つ (x_0, y_0) を求める // 整数解が求まらなければ false を返す // - ★ a = 0 または b = 0 の場合、結果の取り扱いに注意! ★ // - O(log (a + b)) // - 一般解(k は整数) // x = x_0 + k * (b / g) // y = y_0 - k * (a / g) template bool linear_diophantine_equation (T a, T b, T c, T& x_0, T& y_0, T& g) { auto extgcd = [](T a, T b, T& x, T& y) { auto _extgcd = [](auto&& self, T a, T b, T& x, T& y) -> T { if (b == 0) { x = 1; y = 0; return a; } T g = self(self, b, a % b, y, x); y -= (a / b) * x; return g; }; T g = _extgcd(_extgcd, a, b, x, y); if (g < 0) { g = -g; x = -x; y = -y; } return g; }; if (a == 0 && b == 0) { if (c != 0) { return false; } x_0 = y_0 = g = 0; } else if (a == 0) { if (c % b != 0) { return false; } x_0 = 0; y_0 = c / b; g = abs(b); } else if (b == 0) { if (c % a != 0) { return false; } x_0 = c / a; y_0 = 0; g = abs(a); } else { T x_g, y_g; g = extgcd(a, b, x_g, y_g); if (c % g) { return false; } x_0 = x_g * (c / g); y_0 = y_g * (c / g); } return true; } int main() { ios::sync_with_stdio(false); cin.tie(nullptr); cout << fixed << setprecision(15); ll P, Q; input(P, Q); auto func1 = [&]() -> pair { ll a = -Q, b = P, c = 1; ll x_0, y_0, g; bool res = linear_diophantine_equation(a, b, c, x_0, y_0, g); assert(res); ll k = ceil(Q - y_0, Q) - 1; return {x_0 + k * Q, y_0 + k * P}; }; auto func2 = [&]() -> pair { ll a = Q, b = -P, c = 1; ll x_0, y_0, g; bool res = linear_diophantine_equation(a, b, c, x_0, y_0, g); assert(res); ll k = ceil(Q - y_0, Q) - 1; return {x_0 + k * P, y_0 + k * Q}; }; auto [p_L, q_L] = func1(); auto [p_R, q_R] = func2(); debug_pair(make_pair(p_L, q_L)); debug_pair(make_pair(p_R, q_R)); ll ans = q_L + p_L + q_R + p_R; print(ans); return 0; }