#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; using namespace atcoder; typedef long long ll; typedef unsigned long long ull; typedef pair pii; typedef pair pll; typedef vector vi; typedef vector vvi; typedef vector vll; typedef vector vvll; typedef vector vull; typedef vector vvull; typedef vector vstring; typedef complex cd; typedef complex ci; typedef complex cll; string toYN(bool b) { return b ? "Yes" : "No"; } // https://ei1333.github.io/luzhiled/snippets/other/random-number-generator.html struct RandomNumberGenerator { mt19937 mt; RandomNumberGenerator() : mt(chrono::steady_clock::now().time_since_epoch().count()) {} int operator()(int a, int b) { // [a, b) uniform_int_distribution dist(a, b - 1); return dist(mt); } int operator()(int b) { // [0, b) return (*this)(0, b); } }; // loop macro #define REP(i, n) for (int i = 0; i < (int)(n); i++) // read helper template inline void read(int n, std::vector &array) { array = std::vector(n); REP(i, n) { cin >> array[i]; } } template inline void read(int n, int m, std::vector> &matrix) { matrix = std::vector>(n, std::vector(m)); REP(i, n) { REP(j, m) { cin >> matrix[i][j]; } } } // write helper template inline void write(std::vector array) { for (const T &t : array) { cout << t << endl; } } template inline void writeOneLine(std::vector array) { bool first = true; for (const T &t : array) { if (!first) { cout << " "; } cout << t; first = false; } cout << endl; } // vector helper // test by iterator_macro_test.cpp template inline typename vector::const_iterator moreThan( const std::vector &sortedVector, const T &key) { return upper_bound(sortedVector.begin(), sortedVector.end(), key); } template inline typename vector::const_iterator moreThanEq( const std::vector &sortedVector, const T &key) { return lower_bound(sortedVector.begin(), sortedVector.end(), key); } template inline typename vector::const_iterator lessThan( const std::vector &sortedVector, const T &key) { typename vector::const_iterator it = lower_bound(sortedVector.begin(), sortedVector.end(), key); return it == sortedVector.begin() ? sortedVector.end() : --it; } template inline typename vector::const_iterator lessThanEq( const std::vector &sortedVector, const T &key) { typename vector::const_iterator it = upper_bound(sortedVector.begin(), sortedVector.end(), key); return it == sortedVector.begin() ? sortedVector.end() : --it; } // set helper // test by iterator_macro_test.cpp template inline typename set::const_iterator moreThan(const set &container, const T &key) { return container.upper_bound(key); } template inline typename set::const_iterator moreThanEq(const set &container, const T &key) { return container.lower_bound(key); } template inline typename set::const_iterator lessThan(const set &container, const T &key) { typename set::const_iterator it = container.lower_bound(key); return it == container.begin() ? container.end() : --it; } template inline typename set::const_iterator lessThanEq(const set &container, const T &key) { typename set::const_iterator it = container.upper_bound(key); return it == container.begin() ? container.end() : --it; } // multiset helper template inline typename multiset::const_iterator moreThan( const multiset &container, T key) { return container.upper_bound(key); } template inline typename multiset::const_iterator moreThanEq( const multiset &container, T key) { return container.lower_bound(key); } template inline typename multiset::const_iterator lessThan( const multiset &container, T key) { typename set::const_iterator it = container.lower_bound(key); return it == container.begin() ? container.end() : --it; } template inline typename multiset::const_iterator lessThanEq( const multiset &container, T key) { typename set::const_iterator it = container.upper_bound(key); return it == container.begin() ? container.end() : --it; } // map helper // test by iterator_macro_test.cpp template inline typename map::const_iterator moreThan( const map &container, const Key &key) { return container.upper_bound(key); } template inline typename map::const_iterator moreThanEq( const map &container, const Key &key) { return container.lower_bound(key); } template inline typename map::const_iterator lessThan( const map &container, const Key &key) { typename map::const_iterator it = container.lower_bound(key); return it == container.begin() ? container.end() : --it; } template inline typename map::const_iterator lessThanEq( const map &container, const Key &key) { typename map::const_iterator it = container.upper_bound(key); return it == container.begin() ? container.end() : --it; } // https://qiita.com/ganyariya/items/df35d253726269bda436 // // Usage: unordered_map, int, HashPair> mp; struct HashPair { template size_t operator()(const pair &p) const { auto hash1 = hash{}(p.first); auto hash2 = hash{}(p.second); size_t seed = 0; seed ^= hash1 + 0x9e3779b9 + (seed << 6) + (seed >> 2); seed ^= hash2 + 0x9e3779b9 + (seed << 6) + (seed >> 2); return seed; } }; // debug macro // https://www.creativ.xyz/dump-cpp-652/ // // test by dump_macro_test.cpp #define repi(itr, ds) for (auto itr = ds.begin(); itr != ds.end(); itr++) // vector template istream &operator>>(istream &is, vector &vec) { for (T &x : vec) is >> x; return is; } // pair template ostream &operator<<(ostream &os, const pair &pair_var) { os << "(" << pair_var.first << ", " << pair_var.second << ")"; return os; } // vector template ostream &operator<<(ostream &os, const vector &vec) { os << "{"; for (unsigned int i = 0; i < vec.size(); i++) { os << vec[i] << (i + 1 == vec.size() ? "" : ", "); } os << "}"; return os; } // deque template ostream &operator<<(ostream &os, const deque &vec) { os << "{"; for (unsigned int i = 0; i < vec.size(); i++) { os << vec[i] << (i + 1 == vec.size() ? "" : ", "); } os << "}"; return os; } // map template ostream &operator<<(ostream &os, map &map_var) { os << "{"; repi(itr, map_var) { os << *itr; itr++; if (itr != map_var.end()) os << ", "; itr--; } os << "}"; return os; } // set template ostream &operator<<(ostream &os, set &set_var) { os << "{"; repi(itr, set_var) { os << *itr; itr++; if (itr != set_var.end()) os << ", "; itr--; } os << "}"; return os; } // unordered_map template ostream &operator<<(ostream &os, unordered_map &map_var) { os << "{"; repi(itr, map_var) { os << *itr << ", "; } os << "}"; return os; } // unordered_map with HashFunction template ostream &operator<<(ostream &os, unordered_map &map_var) { os << "{"; repi(itr, map_var) { os << *itr << ", "; } os << "}"; return os; } // unordered_set template ostream &operator<<(ostream &os, unordered_set &set_var) { os << "{"; repi(itr, set_var) { os << *itr << ", "; } os << "}"; return os; } // unordered_set with HashFunction template ostream &operator<<(ostream &os, unordered_set &set_var) { os << "{"; repi(itr, set_var) { os << *itr << ", "; } os << "}"; return os; } // dynamic_modint ostream &operator<<(ostream &os, const modint &modint_value) { os << modint_value.val(); return os; } // static_modint template ostream &operator<<(ostream &os, const static_modint &modint_value) { os << modint_value.val(); return os; } #define DUMPOUT cerr void dump_func() { DUMPOUT << endl; } template void dump_func(Head &&head, Tail &&...tail) { DUMPOUT << head; if (sizeof...(Tail) > 0) { DUMPOUT << ", "; } dump_func(std::move(tail)...); } #ifdef DEBUG_ #define DEB #define dump(...) \ DUMPOUT << " " << string(#__VA_ARGS__) << ": " \ << "[" << to_string(__LINE__) << ":" << __FUNCTION__ << "]" << endl \ << " ", \ dump_func(__VA_ARGS__) // vector> template void dumpVV(const vector> &vec) { DUMPOUT << "{" << endl; for (int i = 0; i < vec.size(); i++) { DUMPOUT << " " << vec[i] << endl; } DUMPOUT << "}" << endl; } template void dumpSegtree(const segtree &segtree, int size) { DUMPOUT << "{"; for (int i = 0; i < size; i++) { if (i > 0) { DUMPOUT << ", "; } DUMPOUT << segtree.get(i); } DUMPOUT << "}" << endl; } template void dumpLazySegtree( lazy_segtree &lazySegtree, int size) { DUMPOUT << "{"; for (int i = 0; i < size; i++) { if (i > 0) { DUMPOUT << ", "; } DUMPOUT << lazySegtree.get(i); } DUMPOUT << "}" << endl; } #else #define DEB if (false) #define dump(...) // vector> template void dumpVV(const vector> &vec) { // Do nothing } template void dumpSegtree(const segtree &segtree, int size) { // Do nothing } template void dumpLazySegtree( lazy_segtree &lazySegtree, int size) { // Do nothing } #endif class Solver { private: public: Solver() {} void solve() {} }; // a^0.5 + b^0.5 < x // (a^0.5 + b^0.5)^2 < x^2 // a + 2(ab)^0.5 + b < x^2 // a + b - x^2 < 2(ab)^0.5 // (a + b - x^2)^2 < 4ab // a^2 + b^2 - x^4 + 2ab - 2bx^2 - 2ax^2 < 4ab // a^2 + b^2 - x^4 - 2ab - 2bx^2 - 2ax^2 < 0 // 1 1000000000 1000000000 ll solve(ll a, ll b) { double da = a; double db = b; double sda = sqrt(da); double sdb = sqrt(db); double dxc = sda + sdb; for (ll x = max((ll)dxc + 10, 0LL); true; x--) { ll v1 = a + b - x * x; v1 = v1 * v1; ll v2 = 4 * a * b; dump(da, db, sda, sdb, dxc, x, v1, v2); if (v1 <= v2) { return x + 1; } } } int main(void) { ios::sync_with_stdio(false); cin.tie(nullptr); // Implement here, int n; cin >> n; for (int i = 0; i < n; i++) { int a, b; cin >> a >> b; cout << solve(a, b) << endl; } }