/* -*- 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 p0, int q0) { int d = q - p; if (d == 1) { // (p+x)/(q+x)>=p0/q0 -> q0(p+x)>=p0(q+x) // -> q0*p+q0*x>=p0*q+p0*x -> (q0-p0)x>=p0*q-q0*p ll x = ((ll)p0 * q - (ll)q0 * p + (q0 - p0) - 1) / (q0 - p0); p += x, q += x; } else { 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 * pi); } q += minp - p, p = minp; int g = gcd(p, q); p /= g, q /= g; } } /* 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) { //printf("%d/%d %d/%d\n", up, uq, vp, vq); if (ltpq(up, uq, vp, vq)) forward(up, uq, vp, vq); else forward(vp, vq, up, uq); } printf("%d %d\n", up, uq); } return 0; }