/* -*- coding: utf-8 -*- * * 2183.cc: No.2183 LCA on Rational Tree - yukicoder */ #include #include #include #include using namespace std; /* constant */ const int MAX_P = 35000; const int INF = (1U << 31) - 1; /* typedef */ typedef long long ll; typedef vector vi; typedef pair pii; typedef vector vpii; struct Rat { int p, q; Rat() {} Rat(int _p, int _q): p(_p), q(_q) {} void read() { scanf("%d%d", &p, &q); } int d() const { return q - p; } bool operator==(const Rat r) const { return (ll)p * r.q == (ll)r.p * q; } bool operator!=(const Rat r) const { return (ll)p * r.q != (ll)r.p * q; } bool operator<(const Rat r) const { return (ll)p * r.q < (ll)r.p * q; } bool operator>(const Rat r) const { return (ll)p * r.q > (ll)r.p * q; } }; /* global variables */ bool primes[MAX_P + 1]; vi pnums; /* subroutines */ int gen_primes(int maxp, vi &pnums) { fill(primes, primes + maxp + 1, true); primes[0] = primes[1] = false; int p; for (p = 2; p * p <= maxp; p++) if (primes[p]) { pnums.push_back(p); for (int q = p * p; q <= maxp; q += p) primes[q] = false; } for (; p <= maxp; p++) if (primes[p]) pnums.push_back(p); return (int)pnums.size(); } bool prime_decomp(int n, vi &pnums, vpii& pds) { pds.clear(); int pn = pnums.size(); for (int i = 0; i < pn; i++) { int pi = pnums[i]; if (pi * pi > n) { if (n > 1) pds.push_back(pii(n, 1)); return true; } if (n % pi == 0) { int fi = 0; while (n % pi == 0) n /= pi, fi++; pds.push_back(pii(pi, fi)); } } return false; } template T gcd(T m, T n) { // m >= 0, n >= 0 if (m < n) swap(m, n); while (n > 0) { T r = m % n; m = n; n = r; } return m; } inline Rat reduce(Rat r) { int g = gcd(r.p, r.q); return Rat(r.p / g, r.q / g); } Rat forward(Rat r) { if (r.d() == 1) return r; vpii pds; prime_decomp(r.d(), pnums, pds); int minp = INF; for (auto pd: pds) { int pi = pd.first; minp = min(minp, (r.p / pi + 1) * pi); } return reduce(Rat(minp, r.q + (minp - r.p))); } /* main */ int main() { gen_primes(MAX_P, pnums); int tn; scanf("%d", &tn); while (tn--) { Rat u, v; u.read(), v.read(); while (u != v) { while (u.d() != v.d()) { //printf("%d/%d %d/%d\n", u.p, u.q, v.p, v.q); if (u.d() > v.d()) u = forward(u); else v = forward(v); } if (u > v) swap(u, v); if (u.d() > 1) { Rat u1 = forward(u); u = min(u1, v); } else u = v; } printf("%d %d\n", u.p, u.q); } return 0; }