//#define NDEBUG #pragma warning(disable : 4146) #include 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 auto md_vec(const usize n, const T &value) { return std::vector(n, value); } template auto md_vec(const usize n, Args... args) { return std::vector(n, md_vec(args...)); } template constexpr T difference(const T &a, const T &b) noexcept { return a < b ? b - a : a - b; } template void chmin(T &a, const T &b) noexcept { if (b < a) a = b; } template void chmax(T &a, const T &b) noexcept { if (a < b) a = b; } template class rec_lambda { F f; public: rec_lambda(F &&f_) : f(std::forward(f_)) {} template auto operator()(Args &&... args) const { return f(*this, std::forward(args)...); } }; template 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((n ^ d) < 0 && n % d != 0); } i64 ceil_div(const i64 n, const i64 d) { assert(d != 0); return n / d + static_cast((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 // https://ei1333.github.io/library/math/number-theory/fast-prime-factorization.hpp namespace ei1333 { using namespace std; namespace FastPrimeFactorization { template struct UnsafeMod { UnsafeMod() : x(0) {} UnsafeMod(word _x) : x(init(_x)) {} bool operator==(const UnsafeMod &rhs) const { return x == rhs.x; } bool operator!=(const UnsafeMod &rhs) const { return x != rhs.x; } UnsafeMod &operator+=(const UnsafeMod &rhs) { if ((x += rhs.x) >= mod) x -= mod; return *this; } UnsafeMod &operator-=(const UnsafeMod &rhs) { if (sword(x -= rhs.x) < 0) x += mod; return *this; } UnsafeMod &operator*=(const UnsafeMod &rhs) { x = reduce(dword(x) * rhs.x); return *this; } UnsafeMod operator+(const UnsafeMod &rhs) const { return UnsafeMod(*this) += rhs; } UnsafeMod operator-(const UnsafeMod &rhs) const { return UnsafeMod(*this) -= rhs; } UnsafeMod operator*(const UnsafeMod &rhs) const { return UnsafeMod(*this) *= rhs; } UnsafeMod pow(uint64_t e) const { UnsafeMod ret(1); for (UnsafeMod base = *this; e; e >>= 1, base *= base) { if (e & 1) ret *= base; } return ret; } word get() const { return reduce(x); } static constexpr int word_bits = sizeof(word) * 8; static word modulus() { return mod; } static word init(word w) { return reduce(dword(w) * r2); } static void set_mod(word m) { mod = m; inv = mul_inv(mod); r2 = -dword(mod) % mod; } static word reduce(dword x) { word y = word(x >> word_bits) - word((dword(word(x) * inv) * mod) >> word_bits); return sword(y) < 0 ? y + mod : y; } static word mul_inv(word n, int e = 6, word x = 1) { return !e ? x : mul_inv(n, e - 1, x * (2 - x * n)); } static word mod, inv, r2; word x; }; using uint128_t = __uint128_t; using Mod64 = UnsafeMod; template <> uint64_t Mod64::mod = 0; template <> uint64_t Mod64::inv = 0; template <> uint64_t Mod64::r2 = 0; using Mod32 = UnsafeMod; template <> uint32_t Mod32::mod = 0; template <> uint32_t Mod32::inv = 0; template <> uint32_t Mod32::r2 = 0; bool miller_rabin_primality_test_uint64(uint64_t n) { Mod64::set_mod(n); uint64_t d = n - 1; while (d % 2 == 0) d /= 2; Mod64 e{1}, rev{n - 1}; // http://miller-rabin.appspot.com/ < 2^64 for (uint64_t a : {2, 325, 9375, 28178, 450775, 9780504, 1795265022}) { if (n <= a) break; uint64_t t = d; Mod64 y = Mod64(a).pow(t); while (t != n - 1 && y != e && y != rev) { y *= y; t *= 2; } if (y != rev && t % 2 == 0) return false; } return true; } bool miller_rabin_primality_test_uint32(uint32_t n) { Mod32::set_mod(n); uint32_t d = n - 1; while (d % 2 == 0) d /= 2; Mod32 e{1}, rev{n - 1}; for (uint32_t a : {2, 7, 61}) { if (n <= a) break; uint32_t t = d; Mod32 y = Mod32(a).pow(t); while (t != n - 1 && y != e && y != rev) { y *= y; t *= 2; } if (y != rev && t % 2 == 0) return false; } return true; } bool is_prime(uint64_t n) { if (n == 2) return true; if (n == 1 || n % 2 == 0) return false; if (n < uint64_t(1) << 31) return miller_rabin_primality_test_uint32(n); return miller_rabin_primality_test_uint64(n); } uint64_t pollard_rho(uint64_t n) { if (is_prime(n)) return n; if (n % 2 == 0) return 2; Mod64::set_mod(n); uint64_t d; Mod64 one{1}; for (Mod64 c{one};; c += one) { Mod64 x{2}, y{2}; do { x = x * x + c; y = y * y + c; y = y * y + c; d = gcd((x - y).get(), n); } while (d == 1); if (d < n) return d; } assert(0); } vector prime_factor(uint64_t n) { if (n <= 1) return {}; uint64_t p = pollard_rho(n); if (p == n) return {p}; auto l = prime_factor(p); auto r = prime_factor(n / p); copy(begin(r), end(r), back_inserter(l)); return l; } }; // namespace FastPrimeFactorization } // namespace ei1333 #include template void bitwise_transform(const F f, std::vector &a) { const int n = a.size(); for (int w = 1; w < n; w *= 2) { for (int k = 0; k < n; k += w * 2) { for (int i = 0; i < w; i++) { f(a[k + i], a[k + w + i]); } } } } #include using mint = atcoder::modint998244353; namespace n91 { void main_() { const usize T = scan(); const u64 m = scan(); std::vector ps; { auto f = ei1333::FastPrimeFactorization::prime_factor(m); std::set s; for (auto p : f) s.insert(p); ps.assign(s.begin(), s.end()); } for (const usize loop : rep(0, T)) { const usize n = scan(); mint B = scan(); const mint C = scan(); const mint D = scan(); std::vector v(1 << ps.size(), 1); for (const usize i : rep(0, n)) { u64 A = scan(); if (m % A == 0) { A = m / A; usize j = 0; for (const usize k : rep(0, ps.size())) { if (A % ps[k] == 0) j |= 1 << k; } v[j] *= B + 1; } B = C * B + D; } bitwise_transform([](auto &l, auto &r) { l *= r; }, v); mint ans = 0; for (const usize j : rep(0, v.size())) { ans += (__builtin_parity(j) ? -1 : 1) * v[j]; } if (m == 1) ans -= 1; std::cout << ans.val() << eoln; } } } // 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; }