#nullable enable using System.Numerics; const int Mod = 1000000000; object? Solve() { var t = Int(); var ans = t.Repeat(() => -(Int128)1); for (var i = 0; i < t; i++) { var n = long.Parse(String()); var m = long.Parse(String()); var (d, x, y) = Extensions.ExtendedGCD(Mod, -n); if (d < 0) (d, y) = (-d, -y); if (m % d != 0) continue; var mod = Mod / d; var ins = (Int128)y * (m / d) % mod; if (ins <= 0) ins += mod; ans[i] = ins; } Out(ans); return null; } #region AtCoderIO _io_; var _backend_ = new StandardIOBackend(); _io_ = new(){ Backend = _backend_ }; Out(Solve()); _backend_.Flush(); string String() => _io_.Next(); int Int() => int.Parse(String()); void Out(object? x, string? sep = null) => _io_.Out(x, sep ?? Environment.NewLine); class AtCoderIO { public required StandardIOBackend Backend { get; init; } Memory<string> _input = Array.Empty<string>(); int _iter = 0; public string Next() { while (_iter >= _input.Length) (_input, _iter) = (Backend.ReadLine().Trim().Split(' '), 0); return _input.Span[_iter++]; } public void Out(object? x, string separator) { if (x == null) return; if (x is System.Collections.IEnumerable a and not string) { var objects = a.Cast<object>(); if (!objects.Any()) return; x = string.Join(separator, objects); } Backend.WriteLine(x); } } class StandardIOBackend { readonly StreamReader _sr = new(Console.OpenStandardInput()); readonly StreamWriter _sw = new(Console.OpenStandardOutput()) { AutoFlush = false }; public string ReadLine() => _sr.ReadLine()!; public void WriteLine(object? value) => _sw.WriteLine(value); public void Flush() => _sw.Flush(); } #endregion static class Extensions { public static T[] Repeat<T>(this int time, Func<T> F) => Enumerable.Range(0, time).Select(_ => F()).ToArray(); public static (long d, long x, long y) ExtendedGCD(long a, long b) { var (x0, y0, x1, y1) = (1L, 0L, 0L, 1L); while (b != 0) { var q = a / b; (a, b) = (b, a - q * b); (x0, y0, x1, y1) = (x1, y1, x0 - q * x1, y0 - q * y1); } return (a, x0, y0); } }