// #pragma GCC target("avx2") // #pragma GCC optimize("O3") // #pragma GCC optimize("unroll-loops") // #define INTERACTIVE #include using namespace std; namespace templates { // type using ll = long long; using ull = unsigned long long; using Pii = pair; using Pil = pair; using Pli = pair; using Pll = pair; template using pq = priority_queue; template using qp = priority_queue, greater>; // clang-format off #define vec(T, A, ...) vector A(__VA_ARGS__); #define vvec(T, A, h, ...) vector> A(h, vector(__VA_ARGS__)); #define vvvec(T, A, h1, h2, ...) vector>> A(h1, vector>(h2, vector(__VA_ARGS__))); // clang-format on // for loop #define fori1(a) for (ll _ = 0; _ < (a); _++) #define fori2(i, a) for (ll i = 0; i < (a); i++) #define fori3(i, a, b) for (ll i = (a); i < (b); i++) #define fori4(i, a, b, c) for (ll i = (a); ((c) > 0 || i > (b)) && ((c) < 0 || i < (b)); i += (c)) #define overload4(a, b, c, d, e, ...) e #define fori(...) overload4(__VA_ARGS__, fori4, fori3, fori2, fori1)(__VA_ARGS__) // declare and input // clang-format off #define INT(...) int __VA_ARGS__; inp(__VA_ARGS__); #define LL(...) ll __VA_ARGS__; inp(__VA_ARGS__); #define STRING(...) string __VA_ARGS__; inp(__VA_ARGS__); #define CHAR(...) char __VA_ARGS__; inp(__VA_ARGS__); #define DOUBLE(...) double __VA_ARGS__; STRING(str___); __VA_ARGS__ = stod(str___); #define VEC(T, A, n) vector A(n); inp(A); #define VVEC(T, A, n, m) vector> A(n, vector(m)); inp(A); // clang-format on // const value const ll MOD1 = 1000000007; const ll MOD9 = 998244353; const double PI = acos(-1); // other macro #if !defined(RIN__LOCAL) && !defined(INTERACTIVE) #define endl "\n" #endif #define spa ' ' #define len(A) ll(A.size()) #define all(A) begin(A), end(A) // function vector stoc(string &S) { int n = S.size(); vector ret(n); for (int i = 0; i < n; i++) ret[i] = S[i]; return ret; } string ctos(vector &S) { int n = S.size(); string ret = ""; for (int i = 0; i < n; i++) ret += S[i]; return ret; } template auto min(const T &a) { return *min_element(all(a)); } template auto max(const T &a) { return *max_element(all(a)); } template auto clamp(T &a, const S &l, const S &r) { return (a > r ? r : a < l ? l : a); } template inline bool chmax(T &a, const S &b) { return (a < b ? a = b, 1 : 0); } template inline bool chmin(T &a, const S &b) { return (a > b ? a = b, 1 : 0); } template inline bool chclamp(T &a, const S &l, const S &r) { auto b = clamp(a, l, r); return (a != b ? a = b, 1 : 0); } template T sum(vector &A) { T tot = 0; for (auto a : A) tot += a; return tot; } template vector compression(vector X) { sort(all(X)); X.erase(unique(all(X)), X.end()); return X; } // input and output namespace io { // __int128_t std::ostream &operator<<(std::ostream &dest, __int128_t value) { std::ostream::sentry s(dest); if (s) { __uint128_t tmp = value < 0 ? -value : value; char buffer[128]; char *d = std::end(buffer); do { --d; *d = "0123456789"[tmp % 10]; tmp /= 10; } while (tmp != 0); if (value < 0) { --d; *d = '-'; } int len = std::end(buffer) - d; if (dest.rdbuf()->sputn(d, len) != len) { dest.setstate(std::ios_base::badbit); } } return dest; } // vector template istream &operator>>(istream &is, vector &A) { for (auto &a : A) is >> a; return is; } template ostream &operator<<(ostream &os, vector &A) { for (size_t i = 0; i < A.size(); i++) { os << A[i]; if (i != A.size() - 1) os << ' '; } return os; } // vector> template istream &operator>>(istream &is, vector> &A) { for (auto &a : A) is >> a; return is; } template ostream &operator<<(ostream &os, vector> &A) { for (size_t i = 0; i < A.size(); i++) { os << A[i]; if (i != A.size() - 1) os << endl; } return os; } // pair template istream &operator>>(istream &is, pair &A) { is >> A.first >> A.second; return is; } template ostream &operator<<(ostream &os, pair &A) { os << A.first << ' ' << A.second; return os; } // vector> template istream &operator>>(istream &is, vector> &A) { for (size_t i = 0; i < A.size(); i++) { is >> A[i]; } return is; } template ostream &operator<<(ostream &os, vector> &A) { for (size_t i = 0; i < A.size(); i++) { os << A[i]; if (i != A.size() - 1) os << endl; } return os; } // tuple template struct TuplePrint { static ostream &print(ostream &os, const T &t) { TuplePrint::print(os, t); os << ' ' << get(t); return os; } }; template struct TuplePrint { static ostream &print(ostream &os, const T &t) { os << get<0>(t); return os; } }; template ostream &operator<<(ostream &os, const tuple &t) { TuplePrint::print(os, t); return os; } // io functions void FLUSH() { cout << flush; } void print() { cout << endl; } template void print(Head &&head, Tail &&...tail) { cout << head; if (sizeof...(Tail)) cout << spa; print(std::forward(tail)...); } template void prisep(vector &A, S sep) { int n = A.size(); for (int i = 0; i < n; i++) { cout << A[i]; if (i != n - 1) cout << sep; } cout << endl; } template void priend(T A, S end) { cout << A << end; } template void prispa(T A) { priend(A, spa); } template bool printif(bool f, T A, S B) { if (f) print(A); else print(B); return f; } template void inp(T &...a) { (cin >> ... >> a); } } // namespace io using namespace io; // read graph vector> read_edges(int n, int m, bool direct = false, int indexed = 1) { vector> edges(n, vector()); for (int i = 0; i < m; i++) { INT(u, v); u -= indexed; v -= indexed; edges[u].push_back(v); if (!direct) edges[v].push_back(u); } return edges; } vector> read_tree(int n, int indexed = 1) { return read_edges(n, n - 1, false, indexed); } template vector>> read_wedges(int n, int m, bool direct = false, int indexed = 1) { vector>> edges(n, vector>()); for (int i = 0; i < m; i++) { INT(u, v); T w; inp(w); u -= indexed; v -= indexed; edges[u].push_back({v, w}); if (!direct) edges[v].push_back({u, w}); } return edges; } template vector>> read_wtree(int n, int indexed = 1) { return read_wedges(n, n - 1, false, indexed); } // yes / no namespace yesno { // yes inline bool yes(bool f = true) { cout << (f ? "yes" : "no") << endl; return f; } inline bool Yes(bool f = true) { cout << (f ? "Yes" : "No") << endl; return f; } inline bool YES(bool f = true) { cout << (f ? "YES" : "NO") << endl; return f; } // no inline bool no(bool f = true) { cout << (!f ? "yes" : "no") << endl; return f; } inline bool No(bool f = true) { cout << (!f ? "Yes" : "No") << endl; return f; } inline bool NO(bool f = true) { cout << (!f ? "YES" : "NO") << endl; return f; } // possible inline bool possible(bool f = true) { cout << (f ? "possible" : "impossible") << endl; return f; } inline bool Possible(bool f = true) { cout << (f ? "Possible" : "Impossible") << endl; return f; } inline bool POSSIBLE(bool f = true) { cout << (f ? "POSSIBLE" : "IMPOSSIBLE") << endl; return f; } // impossible inline bool impossible(bool f = true) { cout << (!f ? "possible" : "impossible") << endl; return f; } inline bool Impossible(bool f = true) { cout << (!f ? "Possible" : "Impossible") << endl; return f; } inline bool IMPOSSIBLE(bool f = true) { cout << (!f ? "POSSIBLE" : "IMPOSSIBLE") << endl; return f; } // Alice Bob inline bool Alice(bool f = true) { cout << (f ? "Alice" : "Bob") << endl; return f; } inline bool Bob(bool f = true) { cout << (f ? "Bob" : "Alice") << endl; return f; } // Takahashi Aoki inline bool Takahashi(bool f = true) { cout << (f ? "Takahashi" : "Aoki") << endl; return f; } inline bool Aoki(bool f = true) { cout << (f ? "Aoki" : "Takahashi") << endl; return f; } } // namespace yesno using namespace yesno; } // namespace templates using namespace templates; template struct Modint { int x; Modint() : x(0) {} Modint(int64_t y) { if (y >= 0) x = y % MOD; else x = (y % MOD + MOD) % MOD; } Modint &operator+=(const Modint &p) { x += p.x; if (x >= MOD) x -= MOD; return *this; } Modint &operator-=(const Modint &p) { x -= p.x; if (x < 0) x += MOD; return *this; } Modint &operator*=(const Modint &p) { x = int(1LL * x * p.x % MOD); return *this; } Modint &operator/=(const Modint &p) { *this *= p.inverse(); return *this; } Modint &operator%=(const Modint &p) { assert(p.x == 0); return *this; } Modint operator-() const { return Modint(-x); } Modint &operator++() { x++; if (x == MOD) x = 0; return *this; } Modint &operator--() { if (x == 0) x = MOD; x--; return *this; } Modint operator++(int) { Modint result = *this; ++*this; return result; } Modint operator--(int) { Modint result = *this; --*this; return result; } friend Modint operator+(const Modint &lhs, const Modint &rhs) { return Modint(lhs) += rhs; } friend Modint operator-(const Modint &lhs, const Modint &rhs) { return Modint(lhs) -= rhs; } friend Modint operator*(const Modint &lhs, const Modint &rhs) { return Modint(lhs) *= rhs; } friend Modint operator/(const Modint &lhs, const Modint &rhs) { return Modint(lhs) /= rhs; } friend Modint operator%(const Modint &lhs, const Modint &rhs) { assert(rhs.x == 0); return Modint(lhs); } bool operator==(const Modint &p) const { return x == p.x; } bool operator!=(const Modint &p) const { return x != p.x; } bool operator<(const Modint &rhs) const { return x < rhs.x; } bool operator<=(const Modint &rhs) const { return x <= rhs.x; } bool operator>(const Modint &rhs) const { return x > rhs.x; } bool operator>=(const Modint &rhs) const { return x >= rhs.x; } Modint inverse() const { int a = x, b = MOD, u = 1, v = 0, t; while (b > 0) { t = a / b; a -= t * b; u -= t * v; std::swap(a, b); std::swap(u, v); } return Modint(u); } Modint pow(int64_t k) const { Modint ret(1); Modint y(x); while (k > 0) { if (k & 1) ret *= y; y *= y; k >>= 1; } return ret; } std::pair to_frac(int max_n = 1000) const { int y = x; for (int i = 1; i <= max_n; i++) { if (y <= max_n) { return {y, i}; } else if (MOD - y <= max_n) { return {-(MOD - y), i}; } y = (y + x) % MOD; } return {-1, -1}; } friend std::ostream &operator<<(std::ostream &os, const Modint &p) { return os << p.x; } friend std::istream &operator>>(std::istream &is, Modint &p) { int64_t y; is >> y; p = Modint(y); return (is); } static int get_mod() { return MOD; } }; struct Arbitrary_Modint { int x; static int MOD; static void set_mod(int mod) { MOD = mod; } Arbitrary_Modint() : x(0) {} Arbitrary_Modint(int64_t y) { if (y >= 0) x = y % MOD; else x = (y % MOD + MOD) % MOD; } Arbitrary_Modint &operator+=(const Arbitrary_Modint &p) { x += p.x; if (x >= MOD) x -= MOD; return *this; } Arbitrary_Modint &operator-=(const Arbitrary_Modint &p) { x -= p.x; if (x < 0) x += MOD; return *this; } Arbitrary_Modint &operator*=(const Arbitrary_Modint &p) { x = int(1LL * x * p.x % MOD); return *this; } Arbitrary_Modint &operator/=(const Arbitrary_Modint &p) { *this *= p.inverse(); return *this; } Arbitrary_Modint &operator%=(const Arbitrary_Modint &p) { assert(p.x == 0); return *this; } Arbitrary_Modint operator-() const { return Arbitrary_Modint(-x); } Arbitrary_Modint &operator++() { x++; if (x == MOD) x = 0; return *this; } Arbitrary_Modint &operator--() { if (x == 0) x = MOD; x--; return *this; } Arbitrary_Modint operator++(int) { Arbitrary_Modint result = *this; ++*this; return result; } Arbitrary_Modint operator--(int) { Arbitrary_Modint result = *this; --*this; return result; } friend Arbitrary_Modint operator+(const Arbitrary_Modint &lhs, const Arbitrary_Modint &rhs) { return Arbitrary_Modint(lhs) += rhs; } friend Arbitrary_Modint operator-(const Arbitrary_Modint &lhs, const Arbitrary_Modint &rhs) { return Arbitrary_Modint(lhs) -= rhs; } friend Arbitrary_Modint operator*(const Arbitrary_Modint &lhs, const Arbitrary_Modint &rhs) { return Arbitrary_Modint(lhs) *= rhs; } friend Arbitrary_Modint operator/(const Arbitrary_Modint &lhs, const Arbitrary_Modint &rhs) { return Arbitrary_Modint(lhs) /= rhs; } friend Arbitrary_Modint operator%(const Arbitrary_Modint &lhs, const Arbitrary_Modint &rhs) { assert(rhs.x == 0); return Arbitrary_Modint(lhs); } bool operator==(const Arbitrary_Modint &p) const { return x == p.x; } bool operator!=(const Arbitrary_Modint &p) const { return x != p.x; } bool operator<(const Arbitrary_Modint &rhs) { return x < rhs.x; } bool operator<=(const Arbitrary_Modint &rhs) { return x <= rhs.x; } bool operator>(const Arbitrary_Modint &rhs) { return x > rhs.x; } bool operator>=(const Arbitrary_Modint &rhs) { return x >= rhs.x; } Arbitrary_Modint inverse() const { int a = x, b = MOD, u = 1, v = 0, t; while (b > 0) { t = a / b; a -= t * b; u -= t * v; std::swap(a, b); std::swap(u, v); } return Arbitrary_Modint(u); } Arbitrary_Modint pow(int64_t k) const { Arbitrary_Modint ret(1); Arbitrary_Modint y(x); while (k > 0) { if (k & 1) ret *= y; y *= y; k >>= 1; } return ret; } friend std::ostream &operator<<(std::ostream &os, const Arbitrary_Modint &p) { return os << p.x; } friend std::istream &operator>>(std::istream &is, Arbitrary_Modint &p) { int64_t y; is >> y; p = Arbitrary_Modint(y); return (is); } static int get_mod() { return MOD; } }; int Arbitrary_Modint::MOD = 998244353; using modint9 = Modint<998244353>; using modint1 = Modint<1000000007>; using modint = Arbitrary_Modint; using mint = modint9; // return sum_{i=0}^{n-1} floor((a*i+b)/m) template T floor_sum(T n, T m, T a, T b) { if (a < 0) { return floor_sum(n, m, -a, b + (n - 1) * a); } T ret = 0; while (1) { if (a >= m) { ret += ((n - 1) * n) / 2 * (a / m); a %= m; } if (b >= m) { ret += n * (b / m); b %= m; } T y = (a * n + b) / m; if (y == 0) return ret; T x = y * m - b; ret += (n - (x + a - 1) / a) * y; T nn = y; T nm = a; T na = m; T nb = (-x % a + a) % a; n = nn; m = nm; a = na; b = nb; } } void solve() { LL(n, m); VEC(ll, D, n); mint ans = 0; vec(mint, C, n); vec(mint, invC, n); mint prod = 1; fori(i, n) { C[i] = m / D[i]; invC[i] = mint(1) / C[i]; prod *= C[i]; } // fori(i, n) fori(j, i + 1, n) { // ll r = m / D[i]; // ans += floor_sum(r, D[j], D[i], D[i] - 1) / C[i] / C[j]; // } auto dc = [&](auto &&self, int l, int r) -> void { if (r - l <= 100) { fori(i, l, r) fori(j, i + 1, r) { ll r_ = m / D[i]; ans += floor_sum(r_, D[j], D[i], D[i] - 1) * invC[i] * invC[j]; } return; } ll mid = (l + r) / 2; self(self, l, mid); self(self, mid, r); unordered_map cnt; fori(i, l, mid) { cnt[D[i]] += invC[i]; } vec(mint, tot, m + 1, 0); for (auto [k, v] : cnt) { fori(i, k, m + 1, k) { tot[i] += v; } } fori(i, m - 1, -1, -1) { tot[i] += tot[i + 1]; } unordered_map cnt2; fori(i, mid, r) { cnt2[D[i]] += invC[i]; } vec(mint, tot2, m, 0); for (auto [k, v] : cnt2) { fori(i, k, m, k) { tot2[i] += v; } } fori(i, 1, m + 1) { ans += tot[i] * tot2[i - 1]; } }; dc(dc, 0, n); ans *= prod; print(ans); } int main() { #ifndef INTERACTIVE std::cin.tie(0)->sync_with_stdio(0); #endif // std::cout << std::fixed << std::setprecision(12); int t; t = 1; // std::cin >> t; while (t--) solve(); return 0; } // // #pragma GCC target("avx2") // // #pragma GCC optimize("O3") // // #pragma GCC optimize("unroll-loops") // // #define INTERACTIVE // // #include "kyopro-cpp/template.hpp" // // #include "misc/Modint.hpp" // using mint = modint9; // #include "math/floor_sum.hpp" // // void solve() { // LL(n, m); // VEC(ll, D, n); // mint ans = 0; // // vec(mint, C, n); // vec(mint, invC, n); // mint prod = 1; // fori(i, n) { // C[i] = m / D[i]; // invC[i] = mint(1) / C[i]; // prod *= C[i]; // } // // // fori(i, n) fori(j, i + 1, n) { // // ll r = m / D[i]; // // ans += floor_sum(r, D[j], D[i], D[i] - 1) / C[i] / C[j]; // // } // // auto dc = [&](auto &&self, int l, int r) -> void { // if (r - l <= 100) { // fori(i, l, r) fori(j, i + 1, r) { // ll r_ = m / D[i]; // ans += floor_sum(r_, D[j], D[i], D[i] - 1) * invC[i] * invC[j]; // } // return; // } // // ll mid = (l + r) / 2; // self(self, l, mid); // self(self, mid, r); // // unordered_map cnt; // fori(i, l, mid) { // cnt[D[i]] += invC[i]; // } // // vec(mint, tot, m + 1, 0); // for (auto [k, v] : cnt) { // fori(i, k, m + 1, k) { // tot[i] += v; // } // } // fori(i, m - 1, -1, -1) { // tot[i] += tot[i + 1]; // } // // unordered_map cnt2; // fori(i, mid, r) { // cnt2[D[i]] += invC[i]; // } // // vec(mint, tot2, m, 0); // for (auto [k, v] : cnt2) { // fori(i, k, m, k) { // tot2[i] += v; // } // } // // fori(i, 1, m + 1) { // ans += tot[i] * tot2[i - 1]; // } // }; // // dc(dc, 0, n); // // ans *= prod; // print(ans); // } // // int main() { // #ifndef INTERACTIVE // std::cin.tie(0)->sync_with_stdio(0); // #endif // // std::cout << std::fixed << std::setprecision(12); // int t; // t = 1; // // std::cin >> t; // while (t--) solve(); // return 0; // }