//#define NDEBUG
#pragma warning(disable : 4146)

#include <bits/stdc++.h>

namespace n91 {

  using i32 = std::int32_t;
  using i64 = std::int64_t;
  using u32 = std::uint32_t;
  using u64 = std::uint64_t;
  using isize = std::ptrdiff_t;
  using usize = std::size_t;
  using f64 = double;

  struct rep {
    struct itr {
      usize i;
      constexpr itr(const usize i) noexcept : i(i) {}
      void operator++() noexcept { ++i; }
      constexpr usize operator*() const noexcept { return i; }
      constexpr bool operator!=(const itr x) const noexcept { return i != x.i; }
    };
    const itr f, l;
    constexpr rep(const usize f, const usize l) noexcept
      : f(std::min(f, l)), l(l) {}
    constexpr auto begin() const noexcept { return f; }
    constexpr auto end() const noexcept { return l; }
  };
  struct revrep {
    struct itr {
      usize i;
      constexpr itr(const usize i) noexcept : i(i) {}
      void operator++() noexcept { --i; }
      constexpr usize operator*() const noexcept { return i; }
      constexpr bool operator!=(const itr x) const noexcept { return i != x.i; }
    };
    const itr f, l;
    constexpr revrep(const usize f, const usize l) noexcept
      : f(l - 1), l(std::min(f, l) - 1) {}
    constexpr auto begin() const noexcept { return f; }
    constexpr auto end() const noexcept { return l; }
  };
  template <class T> auto md_vec(const usize n, const T& value) {
    return std::vector<T>(n, value);
  }
  template <class... Args> auto md_vec(const usize n, Args... args) {
    return std::vector<decltype(md_vec(args...))>(n, md_vec(args...));
  }
  template <class T> constexpr T difference(const T& a, const T& b) noexcept {
    return a < b ? b - a : a - b;
  }
  template <class T> void chmin(T& a, const T& b) noexcept {
    if (b < a)
      a = b;
  }
  template <class T> void chmax(T& a, const T& b) noexcept {
    if (a < b)
      a = b;
  }
  template <class F> class rec_lambda {
    F f;

  public:
    rec_lambda(F&& f_) : f(std::forward<F>(f_)) {}
    template <class... Args> auto operator()(Args &&... args) const {
      return f(*this, std::forward<Args>(args)...);
    }
  };
  template <class T> T scan() {
    T ret;
    std::cin >> ret;
    return ret;
  }
  constexpr char eoln = '\n';

  i64 floor_div(const i64 n, const i64 d) {
    assert(d != 0);
    return n / d - static_cast<i64>((n ^ d) < 0 && n % d != 0);
  }

  i64 ceil_div(const i64 n, const i64 d) {
    assert(d != 0);
    return n / d + static_cast<i64>((n ^ d) >= 0 && n % d != 0);
  }

#ifdef N91_LOCAL
#define OJ_LOCAL(a, b) b
#else
#define OJ_LOCAL(a, b) a
#endif

} // namespace n91

#include <atcoder/convolution>
#include <atcoder/modint>

using mint = atcoder::modint998244353;

namespace n91 {

  std::vector<mint> multipoint_evauation_geometric(std::vector<mint> f,
    const mint a, const mint r,
    const int n) {
    if (n == 0)
      return {};
    const int m = f.size();
    if (m == 0)
      return std::vector<mint>(n, 0);
    {
      mint t = 1;
      for (int i = 0; i < m; i++)
        f[i] *= t, t *= a;
    }
    if (r == 0) {
      std::vector<mint> ret(n, 0);
      for (int i = 0; i < m; i++)
        ret[0] += f[i];
      return ret;
    }
    const int l = 1 << (31 - __builtin_clz(2 * (n + m - 1) - 1));
    std::vector<mint> t(l), it(std::max(n, m));
    {
      mint p = 1, pp = 1;
      for (int i = 0; i < l; i++) {
        t[i] = pp;
        pp *= p;
        p *= r;
      }
    }
    {
      const mint inv = 1 / r;
      mint p = 1, pp = 1;
      for (int i = 0; i < it.size(); i++) {
        it[i] = pp;
        pp *= p;
        p *= inv;
      }
    }
    for (int i = 0; i < m; i++)
      f[i] *= it[i];
    std::reverse(f.begin(), f.end());
    f.resize(l);
    atcoder::internal::butterfly(f);
    atcoder::internal::butterfly(t);
    for (int i = 0; i < l; i++)
      f[i] *= t[i];
    atcoder::internal::butterfly_inv(f);
    const mint c = 1 / mint(l);
    std::vector<mint> ret(n);
    for (int i = 0; i < n; i++)
      ret[i] = f[m - 1 + i] * c * it[i];
    return ret;
  }

  void solve() {
    const mint a = scan<u32>();
    const u32 n = scan<u32>();
    usize b = 0;
    while ((b + 1) * (b + 1) <= n)
      b++;
    std::vector<mint> f(b);
    for (const usize i : rep(0, b)) {
      f[i] = a.pow(u64(i) * i);
    }
    const auto seq = multipoint_evauation_geometric(f, 1, a.pow(2 * b), b);
    mint ans = 0;
    for (const usize i : rep(0, b)) {
      ans += seq[i] * a.pow(u64(b) * b * i * i);
    }
    for (const usize i : rep(b* b, n)) {
      ans += a.pow(u64(i) * i);
    }
    std::cout << ans.val() << eoln;
  }

  void main_() {
    const usize t = scan<usize>();
    for (const usize i : rep(0, t))
      solve();
  }

} // namespace n91

int main() {
  //*
  std::ios::sync_with_stdio(false);
  std::cin.tie(nullptr);
  //*/
  std::cout << std::fixed << std::setprecision(20);
  n91::main_();
  return 0;
}