#include using namespace std; using LL = long long int; #define incII(i, l, r) for(LL i = (l) ; i <= (r); i++) #define incID(i, l, r) for(LL i = (l) ; i < (r); i++) #define incCI(i, l, r) for(LL i = (l) + 1; i <= (r); i++) #define incCD(i, l, r) for(LL i = (l) + 1; i < (r); i++) #define decII(i, l, r) for(LL i = (r) ; i >= (l); i--) #define decID(i, l, r) for(LL i = (r) - 1; i >= (l); i--) #define decCI(i, l, r) for(LL i = (r) ; i > (l); i--) #define decCD(i, l, r) for(LL i = (r) - 1; i > (l); i--) #define inc(i, n) incID(i, 0, n) #define dec(i, n) decID(i, 0, n) #define inc1(i, n) incII(i, 1, n) #define dec1(i, n) decII(i, 1, n) auto inII = [](auto v, auto l, auto r) { return (l <= v && v <= r); }; auto inID = [](auto v, auto l, auto r) { return (l <= v && v < r); }; auto inCI = [](auto v, auto l, auto r) { return (l < v && v <= r); }; auto inCD = [](auto v, auto l, auto r) { return (l < v && v < r); }; #define PB push_back #define EB emplace_back #define MP make_pair #define MT make_tuple #define FI first #define SE second #define FR front() #define BA back() #define ALL(v) v.begin(), v.end() #define RALL(v) v.rbegin(), v.rend() auto setmin = [](auto & a, auto b) { return (b < a ? a = b, true : false); }; auto setmax = [](auto & a, auto b) { return (b > a ? a = b, true : false); }; auto setmineq = [](auto & a, auto b) { return (b <= a ? a = b, true : false); }; auto setmaxeq = [](auto & a, auto b) { return (b >= a ? a = b, true : false); }; #define SC static_cast #define SI(v) SC(v.size()) #define SL(v) SC(v.size()) #define RF(e, v) for(auto & e: v) #define until(e) while(! (e)) #define if_not(e) if(! (e)) #define ef else if #define UR assert(false) #define CT continue #define RV(v) reverse(ALL(v)) auto * IS = & cin; // input elements (as a tuple) template void in_([[maybe_unused]] U & t) { } template void in_(U & t) { (* IS) >> get(t); in_(t); } template auto in() { tuple t; in_, 0, T ...>(t); return t; } // input an array template auto ain() { array a; inc(i, N) { (* IS) >> a[i]; } return a; } // input a (multi-dimensional) vector template T vin() { T v; (* IS) >> v; return v; } template auto vin(N n, M ... m) { vector(m ...))> v(n); inc(i, n) { v[i] = vin(m ...); } return v; } // input multi-column (as a tuple of vector) template void colin_([[maybe_unused]] U & t) { } template void colin_(U & t) { A a; (* IS) >> a; get(t).push_back(a); colin_(t); } template auto colin(int n) { tuple ...> t; inc(i, n) { colin_ ...>, 0, T ...>(t); } return t; } auto * OS = & cout; // output elements void out_([[maybe_unused]] string s) { } template void out_([[maybe_unused]] string s, A && a) { (* OS) << a; } template void out_(string s, A && a, B && ... b) { (* OS) << a << s; out_(s, b ...); } auto outF = [](auto x, auto y, auto z, auto ... a) { (* OS) << x; out_(y, a ...); (* OS) << z << flush; }; auto out = [](auto ... a) { outF("", " " , "\n", a ...); }; auto outS = [](auto ... a) { outF("", " " , " " , a ...); }; auto outL = [](auto ... a) { outF("", "\n", "\n", a ...); }; auto outN = [](auto ... a) { outF("", "" , "" , a ...); }; array SEQ_FMT = { "", " ", "" }; auto & SEQ_BEG = SEQ_FMT[0]; auto & SEQ_MID = SEQ_FMT[1]; auto & SEQ_END = SEQ_FMT[2]; // output a (multi-dimensional) vector template ostream & operator<<(ostream & os, vector const & v) { os << SEQ_BEG; inc(i, SI(v)) { os << (i == 0 ? "" : SEQ_MID) << v[i]; } return (os << SEQ_END); } template void vout_(T && v) { (* OS) << v; } template void vout_(T && v, A a, B ... b) { inc(i, SI(v)) { (* OS) << (i == 0 ? "" : a); vout_(v[i], b ...); } } template void vout(T && v, A a, B ... b) { vout_(v, b ...); (* OS) << a << flush; } // ---- ---- vector prime; vector> prime_factorization(LL x) { assert(x > 0); vector> f; RF(e, prime) { LL i = e; if(i > x) { assert(x == 1); break; } if(i * i > x) { i = x; } if(x % i == 0) { f.EB(i, 0); while(x % i == 0) { f.back().SE++; x /= i; } } } return f; } vector divisors(LL x) { auto pf = prime_factorization(x); vector d = { 1 }; for(auto e: pf) { int ds = d.size(); inc(i, ds) { LL v = d[i]; inc(j, e.SE) { v *= e.FI; d.PB(v); } } } sort(ALL(d)); return d; } const int R = 30'000; int main() { { vector d(R); inc1(i, R) { for(int j = 0; j <= R; j += i) { d[j]++; } if(d[i] == 2) { prime.PB(i); } } } auto divmod = [&](LL a, LL b) -> pair { return { a / b, a % b }; }; auto [Q] = in(); inc(q, Q) { auto [x, y] = in(); if_not(x >= y) { swap(x, y); } auto D = divisors(x + y); LL ans = (x == y ? x - 1 : 0); RF(z, D) { LL a = z - 1; if(x >= a * y) { CT; } auto [D, r1] = divmod(x - y, a - 1); auto [E, r2] = divmod(x + y, a + 1); assert(r2 == 0); if(r1 == 0 && D % 2 == E % 2) { ans++; } } out(ans); } }