#include <cassert>
#include <cstring>
#include <fstream>
#include <iostream>
#include <unordered_map>
#include <utility>

#ifdef PROFILING
#include <chrono>
#endif

constexpr char INPUT_FILE_NAME[]  = "euclid2.in";
constexpr char OUTPUT_FILE_NAME[] = "euclid2.out";

class IO_Base
{
    protected:
        IO_Base()          = default;
        virtual ~IO_Base() = default;

        // https://cplusplus.com/reference/system_error/errc/
        const std::unordered_map<int, std::string> FILE_OPEN_ERROR = {
            {ENOENT, "File does not exist."},
            {EACCES, "Permission denied."},
            {EEXIST, "File already exists."},
            {EISDIR, "File is a directory."},
            {ENOSPC, "No space left on device."},
            {EROFS, "Read-only file system."},
            {ETXTBSY, "Text file busy."},
            {-1, "Unlisted error type."},
            {0, "No error."}
        };

        virtual void Close_IN() = 0;
        virtual void Close_OUT() = 0;

        virtual void PrintError(const char* const  _file_name,
                                const int          _error_num,
                                const std::string& _error_source) = 0;
};

class IO final : IO_Base
{
    // C++ I/O functions: https://en.cppreference.com/w/cpp/io

    protected:
        // The Singleton has a private constructor to prevent direct instantiation.
        IO(const char input_file_name[], const char output_file_name[])
        {
            GetInputStream(input_file_name);
            GetOutputStream(output_file_name);
        }

        // The Singleton has a private destructor to prevent deletion.
        ~IO() override
        {
            is_instance_destroyed() = true;
            Close_IN();
            Close_OUT();
        }

    public:
        // Don't make these nullptr. They are not pointers.
        std::ifstream IN;
        std::ofstream OUT;

        // Delete copy constructor. Singletons should not be cloneable.
        IO(const IO&) = delete;
        // Delete move constructor. Singletons should not be movable.
        IO(const IO&&) = delete;
        // Delete assignment operator. Singletons should not be assignable.
        IO& operator=(const IO&) = delete;

        /* Singleton pattern. Only one instance of the class can exist.
         * Thread safe: Initialization is guaranteed to happen only once.
         * A static member object instance is declared. This object is only created
         * the first time the function is called. Static local variables are
         * guaranteed to be initialized only once, even in multithreaded environments.
         * Subsequent calls to GetInstance() simply return the existing instance object.
         * Returning reference instead of pointer further discourages attempts to delete.
         */
        static IO& GetInstance(const char input_file_name[], const char output_file_name[])
        {
            static IO io_Instance(input_file_name, output_file_name);

            if (is_instance_destroyed())
            {
                // We check for The Dead Reference Problem.
                // Our singleton is designed to only be destroyed at program termination.
                std::cerr << "ERROR: Attempt to access destroyed singleton instance." << std::endl;
                assert(false);
            }

            return io_Instance;
        }

    private:
        static bool& is_instance_destroyed()
        {
            /* This variable is used to check for The Dead Reference Problem
             * by enabling the class to check if its singleton has been destroyed.
             */
            static bool is_instance_destroyed = false;
            return is_instance_destroyed;
        }

        void GetInputStream(const char _input_file_name[])
        {
            IN.open(_input_file_name);
            if (!IN.is_open()) // Check if the open operation failed
            {
                if (IN.fail())
                {
                    PrintError(_input_file_name, errno, "Failed to open input");
                    assert(IN);
                }

                if (IN.bad())
                {
                    PrintError(_input_file_name, errno, "Fatal I/O error: bad-bit is set in input");
                    assert(IN);
                }
            }
        }

        void GetOutputStream(const char _output_file_name[])
        {
            OUT.open(_output_file_name);
            if (!OUT.is_open()) // Check if the open operation failed
            {
                if (OUT.fail())
                {
                    PrintError(_output_file_name, errno, "Failed to open output");
                    assert(OUT);
                }

                if (OUT.bad())
                {
                    PrintError(_output_file_name, errno, "Fatal I/O error: bad-bit is set in output");
                    assert(OUT);
                }
            }
        }

        void Close_IN() override final
        {
            IN.close();
        }

        void Close_OUT() override final
        {
            OUT.close();
        }

        void PrintError(const char* const  _file_name,
                        const int          _error_num,
                        const std::string& _error_source) final override
        {
            int error_code = -1;
            if (FILE_OPEN_ERROR.find(_error_num) != FILE_OPEN_ERROR.end())
            {
                error_code = _error_num;
            }

            std::cerr << _error_source << " file: " << _file_name << "\n"
                    << "ERROR: " << strerror(errno) << "\n"
                    << "       " << FILE_OPEN_ERROR.at(error_code) << std::endl;
        }
};

#ifdef PROFILING
class Profiling
{
    private:
        std::chrono::time_point<std::chrono::system_clock> time_begin, time_end;
        std::chrono::duration<double, std::nano>           duration_nano = std::chrono::nanoseconds(0);
        const char*                                        functionName;
        const char*                                        comment;

    public:
        explicit Profiling(const char* _functionName, const char* _comment = "")
            : functionName(_functionName), comment(_comment)
        {
            Begin_Profiling();
        }

        void Begin_Profiling()
        {
            time_begin = std::chrono::high_resolution_clock::now();
        }

        void End_Profiling()
        {
            time_end = std::chrono::high_resolution_clock::now();

            /* Getting number of nanoseconds as a double. */
            duration_nano = std::chrono::duration_cast<std::chrono::nanoseconds>(time_end - time_begin);

            Show_Profiling_Results();
        }

        void Show_Profiling_Results() const
        {
            std::cout << functionName << " : "
                    << duration_nano.count() / 1'000'000'000 << "s | "
                    << duration_nano.count() / 1'000'000 << "ms | "
                    << duration_nano.count() / 1'000 << "\xE6s | "
                    << duration_nano.count() << "ns\n"
                    << "             " << comment << "\n";
        }
};
#endif

/* Using Euclid's algorithm to find the greatest common divisor (gcd).
 * https://crypto.stanford.edu/pbc/notes/numbertheory/euclid.html
 * https://en.algorithmica.org/hpc/algorithms/gcd/
 * https://www.infoarena.ro/algoritmul-lui-euclid
 */
unsigned int euclid(unsigned int a, unsigned int b)
{
    if (b > a)
    {
        std::swap(a, b);
    }

    unsigned int remainder;

    while (b > 0)
    {
        remainder = a % b;
        a         = b;
        b         = remainder;
    }

    return a;
}

/* Using Stein's algorithm to find the greatest common divisor (gcd).
 * https://en.algorithmica.org/hpc/algorithms/gcd/
 * https://en.wikipedia.org/wiki/Binary_GCD_algorithm
 */
unsigned int stein(int a, int b)
{
    if (a == 0) return b;
    if (b == 0) return a;

    int a_trailingzeros   = __builtin_ctz(a);
    int b_trailingzeros   = __builtin_ctz(b);
    int min_trailingzeros = std::min(a_trailingzeros, b_trailingzeros);
    b >>= b_trailingzeros;

    int difference;

    while (a != 0)
    {
        a >>= a_trailingzeros;
        difference      = std::abs(a - b);
        a_trailingzeros = __builtin_ctz(difference);
        b               = std::min(a, b);
        a               = difference;
    }

    return b << min_trailingzeros;
}

int main()
{
    #ifdef PROFILING
    Profiling profiling = Profiling(__PRETTY_FUNCTION__, "gcd(a, b)");
    #endif

    IO& io = IO::GetInstance(INPUT_FILE_NAME, OUTPUT_FILE_NAME);

    unsigned T_counter; // 1 ≤ T ≤ 100 000
    unsigned a, b;      // 2 ≤ a, b ≤ 2 * 10^9

    io.IN >> T_counter;

    while (T_counter--)
    {
        io.IN >> a >> b;
        if (T_counter % 2)
            io.OUT << euclid(a, b) << "\n";
        else
            io.OUT << stein(static_cast<int>(a), static_cast<int>(b)) << "\n";
    }

    #ifdef PROFILING
    profiling.End_Profiling();
    #endif

    return 0;
}