#include using namespace std; using lint = long long; using pint = pair; using plint = pair; struct fast_ios { fast_ios(){ cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(20); }; } fast_ios_; #define ALL(x) (x).begin(), (x).end() #define FOR(i, begin, end) for(int i=(begin),i##_end_=(end);i=i##_begin_;i--) #define REP(i, n) FOR(i,0,n) #define IREP(i, n) IFOR(i,0,n) template void ndarray(vector &vec, int len) { vec.resize(len); } template void ndarray(vector &vec, int len, Args... args) { vec.resize(len); for (auto &v : vec) ndarray(v, args...); } template void ndfill(V &x, const T &val) { x = val; } template void ndfill(vector &vec, const T &val) { for (auto &v : vec) ndfill(v, val); } template bool chmax(T &m, const T q) { if (m < q) {m = q; return true;} else return false; } template bool chmin(T &m, const T q) { if (m > q) {m = q; return true;} else return false; } template pair operator+(const pair &l, const pair &r) { return make_pair(l.first + r.first, l.second + r.second); } template pair operator-(const pair &l, const pair &r) { return make_pair(l.first - r.first, l.second - r.second); } template vector srtunq(vector vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); return vec; } template istream &operator>>(istream &is, vector &vec) { for (auto &v : vec) is >> v; return is; } template ostream &operator<<(ostream &os, const vector &vec) { os << '['; for (auto v : vec) os << v << ','; os << ']'; return os; } #if __cplusplus >= 201703L template istream &operator>>(istream &is, tuple &tpl) { std::apply([&is](auto &&... args) { ((is >> args), ...);}, tpl); return is; } template ostream &operator<<(ostream &os, const tuple &tpl) { std::apply([&os](auto &&... args) { ((os << args << ','), ...);}, tpl); return os; } #endif template ostream &operator<<(ostream &os, const deque &vec) { os << "deq["; for (auto v : vec) os << v << ','; os << ']'; return os; } template ostream &operator<<(ostream &os, const set &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const unordered_set &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const multiset &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const unordered_multiset &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const pair &pa) { os << '(' << pa.first << ',' << pa.second << ')'; return os; } template ostream &operator<<(ostream &os, const map &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const unordered_map &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; } #ifdef HITONANODE_LOCAL #define dbg(x) cerr << #x << " = " << (x) << " (L" << __LINE__ << ") " << __FILE__ << endl #else #define dbg(x) #endif // Sieve of Eratosthenes // (*this)[i] = (divisor of i, greater than 1) // Example: [0, 1, 2, 3, 2, 5, 3, 7, 2, 3, 2, 11, ...] // Complexity: Space O(MAXN), Time (construction) O(MAXNloglogMAXN) struct SieveOfEratosthenes : std::vector { std::vector primes; SieveOfEratosthenes(int MAXN) : std::vector(MAXN + 1) { std::iota(begin(), end(), 0); for (int i = 2; i <= MAXN; i++) { if ((*this)[i] == i) { primes.push_back(i); for (int j = i; j <= MAXN; j += i) (*this)[j] = i; } } } using T = long long int; // Prime factorization for x <= MAXN^2 // Complexity: O(log x) (x <= MAXN) // O(MAXN / logMAXN) (MAXN < x <= MAXN^2) std::map Factorize(T x) { assert(x <= 1LL * (int(size()) - 1) * (int(size()) - 1)); std::map ret; if (x < int(size())) { while (x > 1) { ret[(*this)[x]]++; x /= (*this)[x]; } } else { for (auto p : primes) { while (!(x % p)) x /= p, ret[p]++; if (x == 1) break; } if (x > 1) ret[x]++; } return ret; } std::vector Divisors(T x) { std::vector ret{1}; for (auto p : Factorize(x)) { int n = ret.size(); for (int i = 0; i < n; i++) { for (T a = 1, d = 1; d <= p.second; d++) { a *= p.first; ret.push_back(ret[i] * a); } } } return ret; // Not sorted } // Moebius function Table // return: [0=>0, 1=>1, 2=>-1, 3=>-1, 4=>0, 5=>-1, 6=>1, 7=>-1, 8=>0, ...] std::vector GenerateMoebiusFunctionTable() { std::vector ret(size()); for (int i = 1; i < int(size()); i++) { if (i == 1) ret[i] = 1; else if ((i / (*this)[i]) % (*this)[i] == 0) ret[i] = 0; else ret[i] = -ret[i / (*this)[i]]; } return ret; } }; SieveOfEratosthenes sieve(10000000); lint solve() { lint X, Y; cin >> X >> Y; assert(X > 0 and Y > 0 and X <= 10000000 and Y <= 10000000 and __gcd(X, Y) == 1); if (X * 2 == Y) return 0; if (X * 2 >= Y) X = Y - X; lint ret = 0; if (Y >= X * 2 + 1) { ret += 100000000 / Y; } auto divs = sieve.Divisors(Y); for (auto x : divs) if (x % 2 and x >= 3) { lint m = x / 2; __int128 num = 2 * (m + 1) * m; num *= Y; __int128 den = 2 * m + 1; den *= X; __int128 y = num / den; if (num % den == 0 and 2 * m + 1 < y and y <= 100000000) ret++; } return ret; } int main() { int S; cin >> S; while (S--) cout << solve() << '\n'; }