#include #include #include #include #include using mint = atcoder::modint998244353; namespace details { template constexpr int floor_log2(T n) { int i = 0; while (n) n >>= 1, ++i; return i - 1; } constexpr bool miller_rabin(uint64_t n) { if (n <= 1) return false; uint64_t d = (n - 1) >> __builtin_ctzll(n - 1); if (n == 2 or n == 3 or n == 5 or n == 7) { return true; } if (n % 2 == 0 or n % 3 == 0 or n % 5 == 0 or n % 7 == 0) { return false; } for (uint64_t p : { 2U, 325U, 9375U, 28178U, 450775U, 9780504U, 1795265022U }) { p %= n; if (p == 0) { continue; } uint64_t y = 1; for (uint64_t d2 = d; d2; d2 >>= 1) { if (d2 & 1) { y = __uint128_t(y) * p % n; } p = __uint128_t(p) * p % n; } if (y == 1) { continue; } for (uint64_t t = d; y != n - 1; t <<= 1) { y = __uint128_t(y) * y % n; if (y == 1 or t == n - 1) { return false; } } } return true; } uint64_t pollard_rho(uint64_t n) { const uint64_t m = uint64_t(1) << (floor_log2(n) / 5); static std::mt19937_64 rng{ std::random_device{}() }; std::uniform_int_distribution dist(0, n - 1); while (true) { uint64_t c = dist(rng); auto f = [&](uint64_t x) -> uint64_t { return (__uint128_t(x) * x + c) % n; }; uint64_t x, y = 2, ys, q = 1, g = 1; for (uint64_t r = 1; g == 1; r <<= 1) { x = y; for (uint64_t i = 0; i < r; ++i) { y = f(y); } for (uint64_t k = 0; k < r and g == 1; k += m) { ys = y; for (uint64_t i = 0; i < std::min(m, r - k); ++i) { y = f(y), q = __uint128_t(q) * (x > y ? x - y : y - x) % n; } g = std::gcd(q, n); } } if (g == n) { g = 1; while (g == 1) { ys = f(ys), g = std::gcd(x > ys ? x - ys : ys - x, n); } } if (g < n) { if (miller_rabin(g)) { return g; } if (uint64_t d = n / g; miller_rabin(d)) { return d; } return pollard_rho(g); } } } } std::vector> factorize(uint64_t n) { std::vector> res; if ((n & 1) == 0) { int q = 0; do ++q, n >>= 1; while ((n & 1) == 0); res.emplace_back(2, q); } for (uint64_t p = 3; p * p <= n; p += 2) { if (p >= 101 and n >= 1 << 20) { while (n > 1) { if (details::miller_rabin(n)) { res.emplace_back(std::exchange(n, 1), 1); } else { p = details::pollard_rho(n); int q = 0; do ++q, n /= p; while (n % p == 0); res.emplace_back(p, q); } } break; } if (n % p == 0) { int q = 0; do ++q, n /= p; while (n % p == 0); res.emplace_back(p, q); } } if (n > 1) { res.emplace_back(n, 1); } return res; } std::vector prime_factors(uint64_t m) { std::vector res; for (const auto &prime_power : factorize(m)) { res.push_back(prime_power.first); } return res; } mint solve(uint32_t n, uint64_t m, std::vector pf, std::vector a, std::vector w) { const uint32_t k = pf.size(); std::vector zeta(1 << k, 1); for (uint32_t i = 0; i < n; ++i) if (m % a[i] == 0) { uint32_t t = 0; for (uint32_t j = 0; j < k; ++j) { uint64_t p = pf[j]; if ((m / p) % a[i] != 0) { t |= 1 << j; } } zeta[t] *= 1 + w[i]; } // Zeta transform for (uint32_t block = 1; block < zeta.size(); block *= 2) { for (uint32_t offset = 0; offset < zeta.size(); offset += 2 * block) { for (uint32_t i = 0; i < block; ++i) { zeta[offset + block + i] *= zeta[offset + i]; } } } mint ans = 0; for (uint32_t s = 0; s < zeta.size(); ++s) { if ((k - __builtin_popcount(s)) & 1) { ans -= zeta[s]; } else { ans += zeta[s]; } } return ans - (m == 1); } int main() { std::ios::sync_with_stdio(false); std::cin.tie(nullptr); uint32_t t; uint64_t m; std::cin >> t >> m; std::vector pf = prime_factors(m); for (uint32_t testcase = 0; testcase < t; ++testcase) { uint32_t n; std::cin >> n; uint32_t x0, c, d; std::cin >> x0 >> c >> d; std::vector w(n); w[0] = x0; for (uint32_t i = 1; i < n; ++i) { w[i] = (c * mint(w[i - 1]) + d).val(); } std::vector a(n); for (auto& e : a) std::cin >> e; std::cout << solve(n, m, pf, a, w).val() << '\n'; } return 0; }