/* -*- 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 = 1 << 30; /* typedef */ typedef long long ll; typedef vector vi; typedef pair pii; typedef vector vpii; /* 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 bool ltpq(int p0, int q0, int p1, int q1) { return (ll)p0 * q1 < (ll)p1 * q0; } void forward(int &p, int &q, int vp, int vq) { int d = q - p; // (p+x)/(q+x)>=vp/vq -> vq(p+x)>=vp(q+x) // -> vq*p+vq*x>=vp*q+vp*x -> (vq-vp)x>=vp*q-vq*p ll x = ((ll)vp * q - (ll)vq * p + (vq - vp) - 1) / (vq - vp); int p0 = p + x, q0 = q + x; int g0 = gcd(p0, q0); p0 /= g0, q0 /= g0; if (d > 1) { vpii pds; prime_decomp(d, pnums, pds); int minp = INF; for (auto pd: pds) { int pi = pd.first; minp = min(minp, (p / pi + 1) * pi); } int p1 = minp, q1 = q + (minp - p); int g1 = gcd(p1, q1); p1 /= g1, q1 /= g1; if (ltpq(p1, q1, p0, q0)) p0 = p1, q0 = q1; } p = p0, q = q0; } /* main */ int main() { gen_primes(MAX_P, pnums); int tn; scanf("%d", &tn); while (tn--) { int up, uq, vp, vq; scanf("%d%d%d%d", &up, &uq, &vp, &vq); while (up != vp || uq != vq) { if (ltpq(up, uq, vp, vq)) { //printf("%d/%d < %d/%d\n", up, uq, vp, vq); forward(up, uq, vp, vq); } else { //printf("%d/%d >= %d/%d\n", up, uq, vp, vq); forward(vp, vq, up, uq); } } printf("%d %d\n", up, uq); } return 0; }