// swap 忘れ

#include <array>
#include <iostream>
#include <vector>

#include <atcoder/modint>

using mint = atcoder::modint998244353;

template <typename T, size_t N, size_t M>
using Matrix = std::array<std::array<T, N>, M>;

template <typename T, size_t N, size_t M, size_t K>
Matrix<T, N, K> operator*(const Matrix<T, N, M>& A, const Matrix<T, M, K>& B) {
    Matrix<T, N, K> C{};
    for (size_t i = 0; i < N; ++i) for (size_t j = 0; j < M; ++j) for (size_t k = 0; k < K; ++k) {
        C[i][k] += A[i][j] * B[j][k];
    }
    return C;
}
template <typename T, size_t N, size_t M>
std::array<T, N> operator*(const Matrix<T, N, M>& A, const std::array<T, M>& x) {
    std::array<T, N> y{};
    for (size_t i = 0; i < N; ++i) for (size_t j = 0; j < M; ++j) {
        y[i] += A[i][j] * x[j];
    }
    return y;
}

template <typename T, size_t N>
Matrix<T, N, N> pow(Matrix<T, N, N> A, unsigned long long k) {
    Matrix<T, N, N> B{};
    for (size_t i = 0; i < N; ++i) B[i][i] = 1;
    for (; k; k >>= 1) {
        if (k & 1) B = B * A;
        A = A * A;
    }
    return B;
}

constexpr size_t MAX_N = 10000000;

std::array<mint, MAX_N + 1> g;

void init_g() {
    g.fill(0);
    g[0] = 1;
    for (size_t i = 1; i <= MAX_N; ++i) {
        g[i] += g[i - 1] * (2 * i);
        if (i >= 2) {
            g[i] += g[i - 2] * (i - 1);
        }
    }
}

mint solve(uint32_t n, uint64_t m) {
    if (n == 0) {
        return 1;
    }
    Matrix<mint, 2, 2> A{
        0, 1,
        n, 2 * n + 1
    };
    mint fn1 = g[n - 1], fn = g[n];
    auto [fm1, fm] = pow(A, m - n) * std::array<mint, 2> { fn1, fn };
    return fm1 * fn1 * n + fm * fn;
}

int main() {
    std::ios::sync_with_stdio(false);
    std::cin.tie(nullptr);

    init_g();

    uint32_t t;
    std::cin >> t;
    for (uint32_t case_id = 0; case_id < t; ++case_id) {
        uint32_t n;
        uint64_t m;
        std::cin >> n >> m;

        std::cout << solve(n, m).val() << '\n';
    }
}