#line 1 "main.cpp" #include<bits/stdc++.h> using namespace std; #ifdef LOCAL #include <debug.hpp> #define debug(...) debug_print::multi_print(#__VA_ARGS__, __VA_ARGS__) #else #define debug(...) (static_cast<void>(0)) #endif //#pragma GCC target("avx,avx2") //#pragma GCC optimize("O3") //#pragma GCC optimize("unroll-loops") using ll = long long; using ull = unsigned long long; using ld = long double; using pll = pair<ll,ll>; using pii = pair<int,int>; using vi = vector<int>; using vvi = vector<vi>; using vvvi = vector<vvi>; using vl = vector<ll>; using vvl = vector<vl>; using vvvl = vector<vvl>; using vul = vector<ull>; using vpii = vector<pii>; using vvpii = vector<vpii>; using vpll = vector<pll>; using vs = vector<string>; template<class T> using pq = priority_queue<T,vector<T>, greater<T>>; #define overload4(_1, _2, _3, _4, name, ...) name #define overload3(a,b,c,name,...) name #define rep1(n) for (ll UNUSED_NUMBER = 0; UNUSED_NUMBER < (n); ++UNUSED_NUMBER) #define rep2(i, n) for (ll i = 0; i < (n); ++i) #define rep3(i, a, b) for (ll i = (a); i < (b); ++i) #define rep4(i, a, b, c) for (ll i = (a); i < (b); i += (c)) #define rep(...) overload4(__VA_ARGS__, rep4, rep3, rep2, rep1)(__VA_ARGS__) #define rrep1(n) for(ll i = (n) - 1;i >= 0;i--) #define rrep2(i,n) for(ll i = (n) - 1;i >= 0;i--) #define rrep3(i,a,b) for(ll i = (b) - 1;i >= (a);i--) #define rrep4(i,a,b,c) for(ll i = (a) + ((b)-(a)-1) / (c) * (c);i >= (a);i -= c) #define rrep(...) overload4(__VA_ARGS__, rrep4, rrep3, rrep2, rrep1)(__VA_ARGS__) #define all1(i) begin(i) , end(i) #define all2(i,a) begin(i) , begin(i) + a #define all3(i,a,b) begin(i) + a , begin(i) + b #define all(...) overload3(__VA_ARGS__, all3, all2, all1)(__VA_ARGS__) #define sum(...) accumulate(all(__VA_ARGS__),0LL) template<class T> bool chmin(T &a, const T &b){ if(a > b){ a = b; return 1; } else return 0; } template<class T> bool chmax(T &a, const T &b){ if(a < b){ a = b; return 1; } else return 0; } template<class T> auto min(const T& a){return *min_element(all(a));} template<class T> auto max(const T& a){return *max_element(all(a));} template<class... Ts> void in(Ts&... t); #define INT(...) int __VA_ARGS__; in(__VA_ARGS__) #define LL(...) ll __VA_ARGS__; in(__VA_ARGS__) #define STR(...) string __VA_ARGS__; in(__VA_ARGS__) #define CHR(...) char __VA_ARGS__; in(__VA_ARGS__) #define DBL(...) double __VA_ARGS__; in(__VA_ARGS__) #define LD(...) ld __VA_ARGS__; in(__VA_ARGS__) #define VEC(type, name, size) vector<type> name(size); in(name) #define VV(type, name, h, w) vector<vector<type>> name(h, vector<type>(w)); in(name) ll intpow(ll a, ll b){ll ans = 1; while(b){if(b & 1) ans *= a; a *= a; b /= 2;} return ans;} ll modpow(ll a, ll b, ll p){ ll ans = 1; a %= p;if(a < 0) a += p;while(b){ if(b & 1) (ans *= a) %= p; (a *= a) %= p; b /= 2; } return ans; } bool is_clamp(ll val,ll low,ll high) {return low <= val && val < high;} void Yes() {cout << "Yes\n";return;} void No() {cout << "No\n";return;} void YES() {cout << "YES\n";return;} void NO() {cout << "NO\n";return;} template <typename T> T floor(T a, T b) {return a / b - (a % b && (a ^ b) < 0);} template <typename T> T ceil(T x, T y) {return floor(x + y - 1, y);} template <typename T> T bmod(T x, T y) {return x - y * floor(x, y);} template <typename T> pair<T, T> divmod(T x, T y) {T q = floor(x, y);return {q, x - q * y};} namespace IO{ #define VOID(a) decltype(void(a)) struct setting{ setting(){cin.tie(nullptr); ios::sync_with_stdio(false);fixed(cout); cout.precision(15);}} setting; template<int I> struct P : P<I-1>{}; template<> struct P<0>{}; template<class T> void i(T& t){ i(t, P<3>{}); } void i(vector<bool>::reference t, P<3>){ int a; i(a); t = a; } template<class T> auto i(T& t, P<2>) -> VOID(cin >> t){ cin >> t; } template<class T> auto i(T& t, P<1>) -> VOID(begin(t)){ for(auto&& x : t) i(x); } template<class T, size_t... idx> void ituple(T& t, index_sequence<idx...>){in(get<idx>(t)...);} template<class T> auto i(T& t, P<0>) -> VOID(tuple_size<T>{}){ituple(t, make_index_sequence<tuple_size<T>::value>{});} #undef VOID } #define unpack(a) (void)initializer_list<int>{(a, 0)...} template<class... Ts> void in(Ts&... t){ unpack(IO :: i(t)); } #undef unpack constexpr long double PI = 3.141592653589793238462643383279L; template <class F> struct REC { F f; REC(F &&f_) : f(forward<F>(f_)) {} template <class... Args> auto operator()(Args &&...args) const { return f(*this, forward<Args>(args)...); }}; //constexpr int mod = 998244353; constexpr int mod = 1000000007; #line 2 "library/math/modlog.hpp" template <typename T> T inv(T a, T p) { T b = p, x = 1, y = 0; while (a) { T q = b / a; swap(a, b %= a); swap(x, y -= q * x); } if(b != 1) return -1; return y < 0 ? y + p : y; } //a^x == b(mod p)を求める int64_t mod_log(int64_t a, int64_t b, int64_t p) { if ((a %= p) < 0) a += p; if ((b %= p) < 0) b += p; int64_t f, g, r = 1 % p; for (f = 0; (g = gcd(a, p)) > 1; ++f) { if (b % g) return (r == b) ? f : -1; b /= g; p /= g; (r *= (a / g)) %= p; } if (p == 1) return f; int64_t ir = inv(r, p); (b *= ir) %= p; int64_t k = 0, ak = 1; unordered_map<int64_t, int64_t> baby; for (; k * k < p; ++k) { if(baby.find(ak) == baby.end()) baby[ak] = k; (ak *= a) %= p; } int64_t iak = inv(ak, p); for (int64_t i = 0; i < k; ++i) { if (baby.find(b) != baby.end()) return f + i * k + baby[b]; (b *= iak) %= p; } return -1; } #line 99 "main.cpp" void solve() { int M = 1000000000; LL(n,m); n %= M; m %= M; m = (M - m) % M; auto d = gcd(n,M); if(m % d) cout << -1 << '\n'; else { debug(inv(n/d,M/d),m/d); int ans = inv(n/d,M/d) * (m/d) % (M/d); if(ans == 0) ans += M / d; cout << ans << '\n'; } } int main() { INT(TT); while(TT--) solve(); }