#include #include #include #include #include #include #include #include #include #include #include #define FOR(i, n, m) for (ll i = n; i < (int)m; i++) #define REP(i, n) FOR(i, 0, n) #define ALL(v) v.begin(), v.end() #define pb push_back using namespace std; using ll = long long; using P = pair; constexpr ll inf = 1000000000; constexpr ll mod = 1000000007; constexpr long double eps = 1e-9; template ostream& operator<<(ostream& os, pair p) { os << to_string(p.first) << " " << to_string(p.second); return os; } template ostream& operator<<(ostream& os, vector& v) { REP(i, v.size()) { if (i) os << " "; os << to_string(v[i]); } return os; } struct modint { ll n; public: modint(const ll n = 0) : n((n % mod + mod) % mod) {} static modint pow(modint a, int m) { modint r = 1; while (m > 0) { if (m & 1) { r *= a; } a = (a * a); m /= 2; } return r; } modint& operator++() { *this += 1; return *this; } modint& operator--() { *this -= 1; return *this; } modint operator++(int) { modint ret = *this; *this += 1; return ret; } modint operator--(int) { modint ret = *this; *this -= 1; return ret; } modint operator~() const { return (this->pow(n, mod - 2)); } // inverse friend bool operator==(const modint& lhs, const modint& rhs) { return lhs.n == rhs.n; } friend bool operator<(const modint& lhs, const modint& rhs) { return lhs.n < rhs.n; } friend bool operator>(const modint& lhs, const modint& rhs) { return lhs.n > rhs.n; } friend modint& operator+=(modint& lhs, const modint& rhs) { lhs.n += rhs.n; if (lhs.n >= mod) lhs.n -= mod; return lhs; } friend modint& operator-=(modint& lhs, const modint& rhs) { lhs.n -= rhs.n; if (lhs.n < 0) lhs.n += mod; return lhs; } friend modint& operator*=(modint& lhs, const modint& rhs) { lhs.n = (lhs.n * rhs.n) % mod; return lhs; } friend modint& operator/=(modint& lhs, const modint& rhs) { lhs.n = (lhs.n * (~rhs).n) % mod; return lhs; } friend modint operator+(const modint& lhs, const modint& rhs) { return modint(lhs.n + rhs.n); } friend modint operator-(const modint& lhs, const modint& rhs) { return modint(lhs.n - rhs.n); } friend modint operator*(const modint& lhs, const modint& rhs) { return modint(lhs.n * rhs.n); } friend modint operator/(const modint& lhs, const modint& rhs) { return modint(lhs.n * (~rhs).n); } }; istream& operator>>(istream& is, modint m) { is >> m.n; return is; } ostream& operator<<(ostream& os, modint m) { os << m.n; return os; } #define MAX_N 3030303 long long extgcd(long long a, long long b, long long& x, long long& y) { long long d = a; if (b != 0) { d = extgcd(b, a % b, y, x); y -= (a / b) * x; } else { x = 1; y = 0; } return d; } long long mod_inverse(long long a, long long m) { long long x, y; if (extgcd(a, m, x, y) == 1) return (m + x % m) % m; else return -1; } vector fact(MAX_N + 1, inf); long long mod_fact(long long n, long long& e) { if (fact[0] == inf) { fact[0] = 1; if (MAX_N != 0) fact[1] = 1; for (ll i = 2; i <= MAX_N; ++i) { fact[i] = (fact[i - 1] * i) % mod; } } e = 0; if (n == 0) return 1; long long res = mod_fact(n / mod, e); e += n / mod; if ((n / mod) % 2 != 0) return (res * (mod - fact[n % mod])) % mod; return (res * fact[n % mod]) % mod; } // return nCk long long mod_comb(long long n, long long k) { if (n < 0 || k < 0 || n < k) return 0; long long e1, e2, e3; long long a1 = mod_fact(n, e1), a2 = mod_fact(k, e2), a3 = mod_fact(n - k, e3); if (e1 > e2 + e3) return 0; return (a1 * mod_inverse((a2 * a3) % mod, mod)) % mod; } using mi = modint; mi linear_sum(mi a, mi b) { mi ret = b * (b + 1) / 2; if (a.n != 0) ret -= (a - 1) * a / 2; return ret; } mi quad_sum(mi a, mi b) { mi ret = b * (b + 1) * (2 * b + 1) / 6; if (a.n != 0) ret -= (a - 1) * a * (2 * a - 1) / 6; return ret; } mi mod_pow(mi a, ll n) { mi ret = 1; mi tmp = a; while (n > 0) { if (n % 2) ret *= tmp; tmp = tmp * tmp; n /= 2; } return ret; } ll gcd(ll a, ll b) { if (b == 0) return a; return gcd(b, a % b); } vector> to_gcd(int x, int y) { vector> ret; for(int i = 0; i <= 2000; i++) { if(i % 2 == 0) { if(y == 0) break; ret.pb({1, -x / y}); x -= x / y * y; } else { if(x == 0) break; ret.pb({2, -y / x}); y -= y / x * x; } } // cout << x << " " << y << endl; if(x > 0 && y == 0) { } else if(x < 0 && y == 0) { ret.pb({2, -1}); ret.pb({1, 2}); ret.pb({2, -1}); } else if(x == 0 && y > 0) { ret.pb({1, 1}); ret.pb({2, -1}); } else { assert(x == 0 && y < 0); ret.pb({1, -1}); ret.pb({2, 1}); } return ret; } void check(vector> v, int a, int b) { for(auto p: v) { if(p.first == 1) { a += p.second * b; } else { b += p.second * a; } } cout << a << " " << b << endl; return; } int main() { ios::sync_with_stdio(false); cin.tie(0); int a, b, c, d; cin >> a >> b >> c >> d; if(a == 0 && b == 0) { if(c == 0 && d == 0) { cout << 0 << endl; return 0; } else { cout << -1 << endl; return 0; } } if(c == 0 && d == 0) { if(a == 0 && b == 0) { cout << 0 << endl; return 0; } else { cout << -1 << endl; return 0; } } int g = gcd(a, b); if(c % g != 0 || d % g != 0) { cout << -1 << endl; return 0; } // ここまで OK vector> ab_to_g = to_gcd(a, b), cd_to_g = to_gcd(c, d); reverse(ALL(cd_to_g)); int g1 = abs(gcd(a, b)), g2 = abs(gcd(c, d)); int k = g2 / g1; if(k != 1) { cout << -1 << endl; return 0; } REP(i, (int)cd_to_g.size()) { cd_to_g[i].second = -cd_to_g[i].second; ab_to_g.push_back(cd_to_g[i]); } check(ab_to_g, a, b); // cout << (int)ab_to_g.size() << endl; // for(auto op: ab_to_g) { // cout << op << endl; // } return 0; }