#line 1 "test.cpp" //#pragma GCC target("avx2") //#pragma GCC optimize("O3") //#pragma GCC optimize("unroll-loops") #include using namespace std; #ifdef LOCAL #include #define debug(...) debug_print::multi_print(#__VA_ARGS__, __VA_ARGS__) #else #define debug(...) (static_cast(0)) #endif using ll = long long; using ld = long double; using pll = pair; using pii = pair; using vi = vector; using vvi = vector; using vvvi = vector; using vl = vector; using vvl = vector; using vvvl = vector; using vpii = vector; using vpll = vector; using vs = vector; template using pq = priority_queue,greater>; #define overload4(_1, _2, _3, _4, name, ...) name #define overload3(a,b,c,name,...) name #define rep1(n) for (ll UNUSED_NUMBER = 0; UNUSED_NUMBER < (n); ++UNUSED_NUMBER) #define rep2(i, n) for (ll i = 0; i < (n); ++i) #define rep3(i, a, b) for (ll i = (a); i < (b); ++i) #define rep4(i, a, b, c) for (ll i = (a); i < (b); i += (c)) #define rep(...) overload4(__VA_ARGS__, rep4, rep3, rep2, rep1)(__VA_ARGS__) #define rrep1(n) for(ll i = (n) - 1;i >= 0;i--) #define rrep2(i,n) for(ll i = (n) - 1;i >= 0;i--) #define rrep3(i,a,b) for(ll i = (b) - 1;i >= (a);i--) #define rrep4(i,a,b,c) for(ll i = (a) + ((b)-(a)-1) / (c) * (c);i >= (a);i -= c) #define rrep(...) overload4(__VA_ARGS__, rrep4, rrep3, rrep2, rrep1)(__VA_ARGS__) #define all1(i) begin(i),end(i) #define all2(i,a) begin(i),begin(i)+a #define all3(i,a,b) begin(i)+a,begin(i)+b #define all(...) overload3(__VA_ARGS__, all3, all2, all1)(__VA_ARGS__) #define sum(...) accumulate(all(__VA_ARGS__),0LL) template bool chmin(T &a, const T &b){ if(a > b){ a = b; return 1; } else return 0; } template bool chmax(T &a, const T &b){ if(a < b){ a = b; return 1; } else return 0; } template auto min(const T& a){ return *min_element(all(a)); } template auto max(const T& a){ return *max_element(all(a)); } template void in(Ts&... t); #define INT(...) int __VA_ARGS__; in(__VA_ARGS__) #define LL(...) ll __VA_ARGS__; in(__VA_ARGS__) #define STR(...) string __VA_ARGS__; in(__VA_ARGS__) #define CHR(...) char __VA_ARGS__; in(__VA_ARGS__) #define DBL(...) double __VA_ARGS__; in(__VA_ARGS__) #define LD(...) ld __VA_ARGS__; in(__VA_ARGS__) #define VEC(type, name, size) vector name(size); in(name) #define VV(type, name, h, w) vector> name(h, vector(w)); in(name) ll intpow(ll a, ll b){ ll ans = 1; while(b){if(b & 1) ans *= a; a *= a; b /= 2;} return ans;} ll modpow(ll a, ll b, ll p){ ll ans = 1; a %= p;while(b){ if(b & 1) (ans *= a) %= p; (a *= a) %= p; b /= 2; } return ans; } ll GCD(ll a,ll b) { if(a == 0 || b == 0) return a + b; if(a % b == 0) return b; else return GCD(b,a%b);} ll LCM(ll a,ll b) { if(a == 0) return b; if(b == 0) return a;return a / GCD(a,b) * b;} namespace IO{ #define VOID(a) decltype(void(a)) struct setting{ setting(){cin.tie(nullptr); ios::sync_with_stdio(false);fixed(cout); cout.precision(12);}} setting; template struct P : P{}; template<> struct P<0>{}; template void i(T& t){ i(t, P<3>{}); } void i(vector::reference t, P<3>){ int a; i(a); t = a; } template auto i(T& t, P<2>) -> VOID(cin >> t){ cin >> t; } template auto i(T& t, P<1>) -> VOID(begin(t)){ for(auto&& x : t) i(x); } template void ituple(T& t, index_sequence){ in(get(t)...);} template auto i(T& t, P<0>) -> VOID(tuple_size{}){ ituple(t, make_index_sequence::value>{});} #undef VOID } #define unpack(a) (void)initializer_list{(a, 0)...} template void in(Ts&... t){ unpack(IO :: i(t)); } #undef unpack //constexpr int mod = 1000000007; constexpr int mod = 998244353; static const double PI = 3.1415926535897932; template struct REC { F f; REC(F &&f_) : f(forward(f_)) {} template auto operator()(Args &&...args) const { return f(*this, forward(args)...); }}; #line 2 "library/math/factorize.hpp" vector> prime_factorization(long long n) { vector> ret; int c = 0; while(n % 2 == 0) { c++; n >>= 1; } if(c) ret.emplace_back(2,c); for(long long i = 3; i * i <= n; i += 2) { c = 0; while(n % i == 0) { n /= i; c++; } if(c) ret.emplace_back(i,c); } if (n != 1) ret.emplace_back(n,1); return ret; } vector divisor(long long n) { vector ret; for(long long i = 1; i * i <= n; i++) { if (n % i == 0) { ret.push_back(i); if(i * i != n) {ret.push_back(n / i);} } } sort(ret.begin(),ret.end()); return ret; } #line 87 "test.cpp" int main() { INT(TT); while(TT--) { INT(p1,q1,p2,q2); int r1 = q1 - p1; int r2 = q2 - p2; auto ret1 = prime_factorization(r1); auto ret2 = prime_factorization(r2); map mp1,mp2; set s1,s2; rep(i,ret1.size()) s1.insert(pii{ret1[i].first,i}); rep(i,ret2.size()) s2.insert(pii{ret2[i].first,i}); int a = p1,b = q1; int cnt = 0; while(b - a > 1 && cnt < 10) { cnt++; mp1[a-b].first = b; int pl = 1e9; int y = 0; for(auto &[x,_]:s1) { if(chmin(pl,x-a%x)) y = x; } a += pl; b += pl; mp1[a-b].second = b - 1; int gc = gcd(a,b); a /= gc; b /= gc; vpii tmp; for(auto &[x,id]:s1) { while(gc % x == 0) { gc /= x; ret1[id].second--; } if(ret1[id].second == 0) tmp.emplace_back(x,id); } rep(i,tmp.size()) s1.erase(tmp[i]); } int c = p2,d = q2; cnt = 0; while(d - c > 1 && cnt < 10) { cnt++; mp2[c-d].first = d; int pl = 1e9; int y = 0; for(auto &[x,_]:s2) { if(chmin(pl,x-c%x)) y = x; } c += pl; d += pl; mp2[c-d].second = d - 1; int gc = gcd(c,d); debug(c,d,gc,pl); c /= gc; d /= gc; vpii tmp; for(auto &[x,id]:s2) { while(gc % x == 0) { gc /= x; ret2[id].second--; } if(ret2[id].second == 0) tmp.emplace_back(x,id); } rep(i,tmp.size()) s2.erase(tmp[i]); } int flg = 0; for(auto [val,p]:mp1) { if(mp2.find(val) != mp2.end()) { if(p.first <= mp2[val].second && p.first >= mp2[val].first) { cout << p.first + val << " " << p.first << '\n'; flg = 1; break; } else if(mp2[val].first <= p.second && mp2[val].first >= p.first) { cout << mp2[val].first + val << " " << mp2[val].first << '\n'; flg = 1; break; } } } if(!flg) { cout << max(a,c) << " " << max(d,b) << '\n'; } } }