#include #include #include #include #include namespace emthrm { template struct Matrix { explicit Matrix(const int m, const int n, const T def = 0) : data(m, std::vector(n, def)) {} int nrow() const { return data.size(); } int ncol() const { return data.front().size(); } Matrix pow(long long exponent) const { const int n = nrow(); Matrix res(n, n, 0), tmp = *this; for (int i = 0; i < n; ++i) { res[i][i] = 1; } for (; exponent > 0; exponent >>= 1) { if (exponent & 1) res *= tmp; tmp *= tmp; } return res; } inline const std::vector& operator[](const int i) const { return data[i]; } inline std::vector& operator[](const int i) { return data[i]; } Matrix& operator=(const Matrix& x) = default; Matrix& operator+=(const Matrix& x) { const int m = nrow(), n = ncol(); for (int i = 0; i < m; ++i) { for (int j = 0; j < n; ++j) { data[i][j] += x[i][j]; } } return *this; } Matrix& operator-=(const Matrix& x) { const int m = nrow(), n = ncol(); for (int i = 0; i < m; ++i) { for (int j = 0; j < n; ++j) { data[i][j] -= x[i][j]; } } return *this; } Matrix& operator*=(const Matrix& x) { const int m = nrow(), l = ncol(), n = x.ncol(); std::vector> res(m, std::vector(n, 0)); for (int i = 0; i < m; ++i) { for (int k = 0; k < l; ++k) { for (int j = 0; j < n; ++j) { res[i][j] += data[i][k] * x[k][j]; } } } data.swap(res); return *this; } Matrix operator+(const Matrix& x) const { return Matrix(*this) += x; } Matrix operator-(const Matrix& x) const { return Matrix(*this) -= x; } Matrix operator*(const Matrix& x) const { return Matrix(*this) *= x; } private: std::vector> data; }; } // namespace emthrm int main() { using mint = atcoder::modint998244353; constexpr int kMaxT = 20000, kMaxN = 10000000; constexpr std::int64_t kMaxM = 1000000000000000000; std::vector dp1(kMaxN + 1, emthrm::Matrix(2, 2)); dp1[0][0][0] = dp1[0][1][1] = 1; for (int i = 0; i < kMaxN; ++i) { dp1[i + 1][0][0] = (i + 1) * 2; dp1[i + 1][0][1] = 1; dp1[i + 1][1][0] = i + 1; dp1[i + 1] *= dp1[i]; } std::vector dp2(kMaxN + 1, emthrm::Matrix(2, 2)); dp2[0][0][0] = dp2[0][1][1] = 1; for (int i = 0; i < kMaxN; ++i) { dp2[i + 1][0][0] = (i + 1) * 2; dp2[i + 1][0][1] = 1; dp2[i + 1][1][0] = i; dp2[i + 1] = dp2[i] * dp2[i + 1]; } int t; std::cin >> t; assert(1 <= t && t <= kMaxT); while (t--) { int n; std::int64_t m; std::cin >> n >> m; assert(0 <= n && n <= kMaxN && 0 <= m && m <= kMaxM); if (n > m) { const int tmp = m; m = n; n = tmp; } emthrm::Matrix matrix(2, 2); matrix[0][0] = n * 2 + 1; matrix[0][1] = 1; matrix[1][0] = n; std::cout << (dp2[n] * matrix.pow(m - n) * dp1[n])[0][0].val() << '\n'; } return 0; }