#pragma GCC optimize("Ofast") #include "bits/stdc++.h" // Begin Header {{{ using namespace std; #ifndef DEBUG #define dump(...) #endif #define all(x) begin(x), end(x) #define rall(x) rbegin(x), rend(x) #define rep(i, b, e) for (intmax_t i = (b), i##_limit = (e); i < i##_limit; ++i) #define repc(i, b, e) for (intmax_t i = (b), i##_limit = (e); i <= i##_limit; ++i) #define repr(i, b, e) for (intmax_t i = (b), i##_limit = (e); i >= i##_limit; --i) #define var(Type, ...) Type __VA_ARGS__; input(__VA_ARGS__) constexpr size_t operator""_zu(unsigned long long value) { return value; }; constexpr intmax_t operator""_jd(unsigned long long value) { return value; }; constexpr uintmax_t operator""_ju(unsigned long long value) { return value; }; constexpr int INF = 0x3f3f3f3f; constexpr intmax_t LINF = 0x3f3f3f3f3f3f3f3f_jd; template > using MaxHeap = priority_queue, Compare>; template > using MinHeap = priority_queue, Compare>; inline void input() {} template inline void input(Head&& head, Tail&&... tail) { cin >> head; input(forward(tail)...); } template ::value, nullptr_t> = nullptr> inline istream& operator>>(istream &is, Container &vs) { for (auto &v: vs) is >> v; return is; } template inline istream& operator>>(istream &is, pair &p) { is >> p.first >> p.second; return is; } inline void output() { cout << "\n"; } template inline void output(Head&& head, Tail&&... tail) { cout << head; if (sizeof...(tail)) cout << " "; output(forward(tail)...); } template ::value, nullptr_t> = nullptr> inline ostream& operator<<(ostream &os, const Container &vs) { static constexpr const char *delim[] = {" ", ""}; for (auto it = begin(vs); it != end(vs); ++it) { os << delim[it == begin(vs)] << *it; } return os; } template inline void join(const Iterator &Begin, const Iterator &End, const string &delim = "\n", const string &last = "\n") { for (auto it = Begin; it != End; ++it) { cout << ((it == Begin) ? "" : delim) << *it; } cout << last; } template inline vector makeVector(const T &init_value, size_t sz) { return vector(sz, init_value); } template inline auto makeVector(const T &init_value, size_t sz, Args... args) { return vector(init_value, args...))>(sz, makeVector(init_value, args...)); } template class FixPoint : Func { public: explicit constexpr FixPoint(Func&& f) noexcept : Func(forward(f)) {} template constexpr decltype(auto) operator()(Args&&... args) const { return Func::operator()(*this, std::forward(args)...); } }; template static inline constexpr decltype(auto) makeFixPoint(Func&& f) noexcept { return FixPoint{forward(f)}; } template struct reverse_t { Container &c; reverse_t(Container &c) : c(c) {} auto begin() { return c.rbegin(); } auto end() { return c.rend(); } }; template auto reversed(Container &c) { return reverse_t(c); } template inline bool chmax(T &a, const T &b) noexcept { return b > a && (a = b, true); } template inline bool chmin(T &a, const T &b) noexcept { return b < a && (a = b, true); } template inline T diff(const T &a, const T &b) noexcept { return a < b ? b - a : a - b; } void operator|=(vector::reference lhs, const bool rhs) { lhs = lhs | rhs; } void ioinit() { ios_base::sync_with_stdio(false); cin.tie(nullptr); cout << fixed << setprecision(10); cerr << fixed << setprecision(10); clog << fixed << setprecision(10); } // }}} End Header // Chinese Remainder Theorem {{{ // find (x, y) s.t. ax + by = gcd(a, b) // |x| <= b, |y| <= a // return gcd(a, b) template T extgcd(T a, T b, T &x, T &y) { T g = a; x = 1, y = 0; if (b != 0) { g = extgcd(b, a % b, y, x); y -= (a / b) * x; } return g; } // When there is no solution: return (0, 0) // otherwise: return (rem, mod) // time complexity: O(n log lcm(ms[i])) pair crt(const vector& rs, const vector& ms) { assert(rs.size() == ms.size()); intmax_t r = 0, m = 1; for (size_t i = 0; i < rs.size(); ++i) { intmax_t p, q; intmax_t g = extgcd(m, ms[i], p, q); if ((rs[i] - r) % g != 0) return make_pair(0, 0); intmax_t t = (rs[i] - r) / g * p % (ms[i] / g); r += m * t; m *= ms[i] / g; } r = (r % m + m) % m; return make_pair(r, m); } // }}} int main() { ioinit(); vector rs(3), ms(3); rep(i, 0, 3) input(rs[i], ms[i]); auto [rem, mod] = crt(rs, ms); dump(rem, mod); if (mod == 0) { output(-1); } else if (all_of(all(rs), [](auto r) { return r == 0; })) { output(mod); } else { output(rem); } return 0; }