// QCFium 法 #pragma GCC target("avx2") #pragma GCC optimize("O3") #pragma GCC optimize("unroll-loops") #ifndef HIDDEN_IN_VS // 折りたたみ用 // 警告の抑制 #define _CRT_SECURE_NO_WARNINGS // ライブラリの読み込み #include using namespace std; // 型名の短縮 using ll = long long; using ull = unsigned long long; // -2^63 ~ 2^63 = 9e18(int は -2^31 ~ 2^31 = 2e9) using pii = pair; using pll = pair; using pil = pair; using pli = pair; using vi = vector; using vvi = vector; using vvvi = vector; using vvvvi = vector; using vl = vector; using vvl = vector; using vvvl = vector; using vvvvl = vector; using vb = vector; using vvb = vector; using vvvb = vector; using vc = vector; using vvc = vector; using vvvc = vector; using vd = vector; using vvd = vector; using vvvd = vector; template using priority_queue_rev = priority_queue, greater>; using Graph = vvi; // 定数の定義 const double PI = acos(-1); int DX[4] = { 1, 0, -1, 0 }; // 4 近傍(下,右,上,左) int DY[4] = { 0, 1, 0, -1 }; int INF = 1001001001; ll INFL = 4004004003094073385LL; // (int)INFL = INF, (int)(-INFL) = -INF; // 入出力高速化 struct fast_io { fast_io() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(18); } } fastIOtmp; // 汎用マクロの定義 #define all(a) (a).begin(), (a).end() #define sz(x) ((int)(x).size()) #define lbpos(a, x) (int)distance((a).begin(), std::lower_bound(all(a), (x))) #define ubpos(a, x) (int)distance((a).begin(), std::upper_bound(all(a), (x))) #define Yes(b) {cout << ((b) ? "Yes\n" : "No\n");} #define rep(i, n) for(int i = 0, i##_len = int(n); i < i##_len; ++i) // 0 から n-1 まで昇順 #define repi(i, s, t) for(int i = int(s), i##_end = int(t); i <= i##_end; ++i) // s から t まで昇順 #define repir(i, s, t) for(int i = int(s), i##_end = int(t); i >= i##_end; --i) // s から t まで降順 #define repe(v, a) for(const auto& v : (a)) // a の全要素(変更不可能) #define repea(v, a) for(auto& v : (a)) // a の全要素(変更可能) #define repb(set, d) for(int set = 0, set##_ub = 1 << int(d); set < set##_ub; ++set) // d ビット全探索(昇順) #define repis(i, set) for(int i = lsb(set), bset##i = set; i < 32; bset##i -= 1 << i, i = lsb(bset##i)) // set の全要素(昇順) #define repp(a) sort(all(a)); for(bool a##_perm = true; a##_perm; a##_perm = next_permutation(all(a))) // a の順列全て(昇順) #define uniq(a) {sort(all(a)); (a).erase(unique(all(a)), (a).end());} // 重複除去 #define EXIT(a) {cout << (a) << endl; exit(0);} // 強制終了 #define inQ(x, y, u, l, d, r) ((u) <= (x) && (l) <= (y) && (x) < (d) && (y) < (r)) // 半開矩形内判定 // 汎用関数の定義 template inline ll powi(T n, int k) { ll v = 1; rep(i, k) v *= n; return v; } template inline bool chmax(T& M, const T& x) { if (M < x) { M = x; return true; } return false; } // 最大値を更新(更新されたら true を返す) template inline bool chmin(T& m, const T& x) { if (m > x) { m = x; return true; } return false; } // 最小値を更新(更新されたら true を返す) template inline T getb(T set, int i) { return (set >> i) & T(1); } template inline T smod(T n, T m) { n %= m; if (n < 0) n += m; return n; } // 非負mod // 演算子オーバーロード template inline istream& operator>>(istream& is, pair& p) { is >> p.first >> p.second; return is; } template inline istream& operator>>(istream& is, vector& v) { repea(x, v) is >> x; return is; } template inline vector& operator--(vector& v) { repea(x, v) --x; return v; } template inline vector& operator++(vector& v) { repea(x, v) ++x; return v; } #endif // 折りたたみ用 #if __has_include() #include using namespace atcoder; #ifdef _MSC_VER #include "localACL.hpp" #endif using mint = modint998244353; //using mint = static_modint<1000000009>; //using mint = modint; // mint::set_mod(m); namespace atcoder { inline istream& operator>>(istream& is, mint& x) { ll x_; is >> x_; x = x_; return is; } inline ostream& operator<<(ostream& os, const mint& x) { os << x.val(); return os; } } using vm = vector; using vvm = vector; using vvvm = vector; using vvvvm = vector; using pim = pair; #endif #ifdef _MSC_VER // 手元環境(Visual Studio) #include "local.hpp" #else // 提出用(gcc) inline int popcount(int n) { return __builtin_popcount(n); } inline int popcount(ll n) { return __builtin_popcountll(n); } inline int lsb(int n) { return n != 0 ? __builtin_ctz(n) : 32; } inline int lsb(ll n) { return n != 0 ? __builtin_ctzll(n) : 64; } inline int msb(int n) { return n != 0 ? (31 - __builtin_clz(n)) : -1; } inline int msb(ll n) { return n != 0 ? (63 - __builtin_clzll(n)) : -1; } #define dump(...) #define dumpel(...) #define dump_list(v) #define dump_mat(v) #define input_from_file(f) #define output_to_file(f) #define Assert(b) { if (!(b)) { vc MLE(1<<30); EXIT(MLE.back()); } } // RE の代わりに MLE を出す #endif // 転倒数といえばフェニック木 mint TLE(int n, int m, vi d) { fenwick_tree ft(m + 1); vm w(n); rep(i, n) w[i] = m / d[i]; // dump(w); vm w_inv(n); rep(i, n) w_inv[i] = 1 / w[i]; mint w_mul = 1; rep(i, n) w_mul *= w[i]; mint res = 0; repir(i, n - 1, 0) { // dump("------- i:", i, "--------"); int x_max = m / d[i] * d[i]; for (int x = x_max; x > 0; x -= d[i]) { // dump("x:", x); mint pres = res; res += ft.sum(0, x) * w_inv[i]; ft.add(x, w_mul * w_inv[i]); // dump(res - pres); // dump(ft); } } return res; } // 倍数のとこしか見ないことを利用 mint TLE2(int n, int m, vi a) { vm w(n); rep(i, n) w[i] = m / a[i]; mint w_mul = 1; rep(i, n) w_mul *= w[i]; vm w_inv(n); rep(i, n) w_inv[i] = 1 / w[i]; // 前計算が激重 vvl coef(m + 1, vl(m + 1)); repi(j, 1, m) repi(d, 1, m) { coef[j][d] = floor_sum(m / d, j, d, d - 1); } dumpel(coef); vm c(m + 1); mint res = 0; rep(i, n) { dump("------- i:", i, "--------"); int j = a[i]; repi(d, 1, m) { mint pres = res; res += c[d] * coef[j][d] * w_inv[i]; dump("d:", d, "add:", res - pres); } c[j] += w_mul * w_inv[i]; } return res; } mint solve(int n, int m, vi a) { vm w(n); rep(i, n) w[i] = m / a[i]; mint w_mul = 1; rep(i, n) w_mul *= w[i]; vm w_inv(n); rep(i, n) w_inv[i] = 1 / w[i]; int TH = int(sqrt(m)); // 前計算の量を削減 vvl coef(m + 1); repi(j, 1, m) { if (j <= TH) coef[j].resize(m + 1); else coef[j].resize(TH + 1); repi(d, 1, sz(coef[j]) - 1) { coef[j][d] = floor_sum(m / d, j, d, d - 1); } } dumpel(coef); vm c(m + 1); vm ans(m + 1); fenwick_tree C(m + 1); mint res = 0; rep(i, n) { dump("------- i:", i, "--------"); int j = a[i]; // 3 通りの解法を使い分けるゴリ押し if (j <= TH) { res += ans[j] * w_inv[i]; } else { repi(d, 1, TH) { res += c[d] * coef[j][d] * w_inv[i]; } for (int k = j + 1; k <= m; k += j) { int k_ub = min(k + j, m + 1); res += ((k - 1) / j) * C.sum(k, k_ub) * w_inv[i]; } for (int k = j; k <= m; k += j) { C.add(k, w_mul * w_inv[i]); } } c[j] += w_mul * w_inv[i]; repi(d, 1, TH) { ans[d] += w_mul * w_inv[i] * coef[d][j]; } dump(c); dump(ans); dump(C); dump(res); } return res; } void bug_find() { #ifdef _MSC_VER // 合わない入力例を見つける. mute_dump = true; mt19937_64 mt; mt.seed((int)time(NULL)); uniform_int_distribution rnd(0LL, 1LL << 60); rep(hoge, 100) { int n = rnd(mt) % 100 + 2; int m = rnd(mt) % 100 + 1; vi d(n); rep(i, n) d[i] = rnd(mt) % m + 1; auto res_naive = TLE(n, m, d); auto res_solve = solve(n, m, d); if (res_naive != res_solve) { cout << "----------error!----------" << endl; cout << "input:" << endl; cout << n << " " << m << endl; cout << d << endl; cout << "results:" << endl; cout << res_naive << endl; cout << res_solve << endl; cout << "--------------------------" << endl; } } mute_dump = false; exit(0); #endif } int main() { // input_from_file("input.txt"); // output_to_file("output.txt"); // bug_find(); int n, m; cin >> n >> m; vi d(n); cin >> d; dump(n, m); dump(d); dump("----"); // dump(TLE(n, m, d)); dump("-----"); // dump(TLE2(n, m, d)); dump("-----"); cout << solve(n, m, d) << endl; }