結果
問題 | No.2959 Dolls' Tea Party |
ユーザー |
![]() |
提出日時 | 2024-11-08 23:36:32 |
言語 | C++23 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 634 ms / 3,000 ms |
コード長 | 37,004 bytes |
コンパイル時間 | 3,917 ms |
コンパイル使用メモリ | 285,396 KB |
実行使用メモリ | 13,824 KB |
最終ジャッジ日時 | 2024-11-08 23:36:57 |
合計ジャッジ時間 | 22,035 ms |
ジャッジサーバーID (参考情報) |
judge4 / judge3 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 4 |
other | AC * 33 |
ソースコード
#line 2 "/Users/noya2/Desktop/Noya2_library/template/template.hpp"using namespace std;#include<bits/stdc++.h>#line 1 "/Users/noya2/Desktop/Noya2_library/template/inout_old.hpp"namespace noya2 {template <typename T, typename U>ostream &operator<<(ostream &os, const pair<T, U> &p){os << p.first << " " << p.second;return os;}template <typename T, typename U>istream &operator>>(istream &is, pair<T, U> &p){is >> p.first >> p.second;return is;}template <typename T>ostream &operator<<(ostream &os, const vector<T> &v){int s = (int)v.size();for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i];return os;}template <typename T>istream &operator>>(istream &is, vector<T> &v){for (auto &x : v) is >> x;return is;}void in() {}template <typename T, class... U>void in(T &t, U &...u){cin >> t;in(u...);}void out() { cout << "\n"; }template <typename T, class... U, char sep = ' '>void out(const T &t, const U &...u){cout << t;if (sizeof...(u)) cout << sep;out(u...);}template<typename T>void out(const vector<vector<T>> &vv){int s = (int)vv.size();for (int i = 0; i < s; i++) out(vv[i]);}struct IoSetup {IoSetup(){cin.tie(nullptr);ios::sync_with_stdio(false);cout << fixed << setprecision(15);cerr << fixed << setprecision(7);}} iosetup_noya2;} // namespace noya2#line 1 "/Users/noya2/Desktop/Noya2_library/template/const.hpp"namespace noya2{const int iinf = 1'000'000'007;const long long linf = 2'000'000'000'000'000'000LL;const long long mod998 = 998244353;const long long mod107 = 1000000007;const long double pi = 3.14159265358979323;const vector<int> dx = {0,1,0,-1,1,1,-1,-1};const vector<int> dy = {1,0,-1,0,1,-1,-1,1};const string ALP = "ABCDEFGHIJKLMNOPQRSTUVWXYZ";const string alp = "abcdefghijklmnopqrstuvwxyz";const string NUM = "0123456789";void yes(){ cout << "Yes\n"; }void no(){ cout << "No\n"; }void YES(){ cout << "YES\n"; }void NO(){ cout << "NO\n"; }void yn(bool t){ t ? yes() : no(); }void YN(bool t){ t ? YES() : NO(); }} // namespace noya2#line 2 "/Users/noya2/Desktop/Noya2_library/template/utils.hpp"#line 6 "/Users/noya2/Desktop/Noya2_library/template/utils.hpp"namespace noya2{unsigned long long inner_binary_gcd(unsigned long long a, unsigned long long b){if (a == 0 || b == 0) return a + b;int n = __builtin_ctzll(a); a >>= n;int m = __builtin_ctzll(b); b >>= m;while (a != b) {int mm = __builtin_ctzll(a - b);bool f = a > b;unsigned long long c = f ? a : b;b = f ? b : a;a = (c - b) >> mm;}return a << std::min(n, m);}template<typename T> T gcd_fast(T a, T b){ return static_cast<T>(inner_binary_gcd(std::abs(a),std::abs(b))); }long long sqrt_fast(long long n) {if (n <= 0) return 0;long long x = sqrt(n);while ((x + 1) * (x + 1) <= n) x++;while (x * x > n) x--;return x;}template<typename T> T floor_div(const T n, const T d) {assert(d != 0);return n / d - static_cast<T>((n ^ d) < 0 && n % d != 0);}template<typename T> T ceil_div(const T n, const T d) {assert(d != 0);return n / d + static_cast<T>((n ^ d) >= 0 && n % d != 0);}template<typename T> void uniq(std::vector<T> &v){std::sort(v.begin(),v.end());v.erase(unique(v.begin(),v.end()),v.end());}template <typename T, typename U> inline bool chmin(T &x, U y) { return (y < x) ? (x = y, true) : false; }template <typename T, typename U> inline bool chmax(T &x, U y) { return (x < y) ? (x = y, true) : false; }template<typename T> inline bool range(T l, T x, T r){ return l <= x && x < r; }} // namespace noya2#line 8 "/Users/noya2/Desktop/Noya2_library/template/template.hpp"#define rep(i,n) for (int i = 0; i < (int)(n); i++)#define repp(i,m,n) for (int i = (m); i < (int)(n); i++)#define reb(i,n) for (int i = (int)(n-1); i >= 0; i--)#define all(v) (v).begin(),(v).end()using ll = long long;using ld = long double;using uint = unsigned int;using ull = unsigned long long;using pii = pair<int,int>;using pll = pair<ll,ll>;using pil = pair<int,ll>;using pli = pair<ll,int>;namespace noya2{/* ~ (. _________ . /) */}using namespace noya2;#line 2 "c.cpp"#line 2 "/Users/noya2/Desktop/Noya2_library/fps998244353/fps998244353.hpp"#line 2 "/Users/noya2/Desktop/Noya2_library/utility/modint.hpp"#line 4 "/Users/noya2/Desktop/Noya2_library/utility/modint.hpp"#line 2 "/Users/noya2/Desktop/Noya2_library/math/prime.hpp"#line 4 "/Users/noya2/Desktop/Noya2_library/math/prime.hpp"namespace noya2 {constexpr long long safe_mod(long long x, long long m) {x %= m;if (x < 0) x += m;return x;}constexpr long long pow_mod_constexpr(long long x, long long n, int m) {if (m == 1) return 0;unsigned int _m = (unsigned int)(m);unsigned long long r = 1;unsigned long long y = safe_mod(x, m);while (n) {if (n & 1) r = (r * y) % _m;y = (y * y) % _m;n >>= 1;}return r;}constexpr bool is_prime_constexpr(int n) {if (n <= 1) return false;if (n == 2 || n == 7 || n == 61) return true;if (n % 2 == 0) return false;long long d = n - 1;while (d % 2 == 0) d /= 2;constexpr long long bases[3] = {2, 7, 61};for (long long a : bases) {long long t = d;long long y = pow_mod_constexpr(a, t, n);while (t != n - 1 && y != 1 && y != n - 1) {y = y * y % n;t <<= 1;}if (y != n - 1 && t % 2 == 0) {return false;}}return true;}template <int n> constexpr bool is_prime_flag = is_prime_constexpr(n);constexpr std::pair<long long, long long> inv_gcd(long long a, long long b) {a = safe_mod(a, b);if (a == 0) return {b, 0};long long s = b, t = a;long long m0 = 0, m1 = 1;while (t) {long long u = s / t;s -= t * u;m0 -= m1 * u;auto tmp = s;s = t;t = tmp;tmp = m0;m0 = m1;m1 = tmp;}if (m0 < 0) m0 += b / s;return {s, m0};}constexpr int primitive_root_constexpr(int m) {if (m == 2) return 1;if (m == 167772161) return 3;if (m == 469762049) return 3;if (m == 754974721) return 11;if (m == 998244353) return 3;int divs[20] = {};divs[0] = 2;int cnt = 1;int x = (m - 1) / 2;while (x % 2 == 0) x /= 2;for (int i = 3; (long long)(i)*i <= x; i += 2) {if (x % i == 0) {divs[cnt++] = i;while (x % i == 0) {x /= i;}}}if (x > 1) {divs[cnt++] = x;}for (int g = 2;; g++) {bool ok = true;for (int i = 0; i < cnt; i++) {if (pow_mod_constexpr(g, (m - 1) / divs[i], m) == 1) {ok = false;break;}}if (ok) return g;}}template <int m> constexpr int primitive_root_flag = primitive_root_constexpr(m);// constexpr long long primitive_root_constexpr(long long m){// if (m == (1LL << 47) - (1LL << 24) + 1) return 3;// return primitive_root_constexpr(static_cast<int>(m));// }} // namespace noya2#line 6 "/Users/noya2/Desktop/Noya2_library/utility/modint.hpp"namespace noya2{struct barrett {unsigned int _m;unsigned long long im;explicit barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {}unsigned int umod() const { return _m; }unsigned int mul(unsigned int a, unsigned int b) const {unsigned long long z = a;z *= b;unsigned long long x = (unsigned long long)((__uint128_t(z) * im) >> 64);unsigned int v = (unsigned int)(z - x * _m);if (_m <= v) v += _m;return v;}};template <int m>struct static_modint {using mint = static_modint;public:static constexpr int mod() { return m; }static mint raw(int v) {mint x;x._v = v;return x;}constexpr static_modint() : _v(0) {}template<std::signed_integral T>constexpr static_modint(T v){long long x = (long long)(v % (long long)(umod()));if (x < 0) x += umod();_v = (unsigned int)(x);}template<std::unsigned_integral T>constexpr static_modint(T v){_v = (unsigned int)(v % umod());}constexpr unsigned int val() const { return _v; }mint& operator++() {_v++;if (_v == umod()) _v = 0;return *this;}mint& operator--() {if (_v == 0) _v = umod();_v--;return *this;}mint operator++(int) {mint result = *this;++*this;return result;}mint operator--(int) {mint result = *this;--*this;return result;}constexpr mint& operator+=(const mint& rhs) {_v += rhs._v;if (_v >= umod()) _v -= umod();return *this;}constexpr mint& operator-=(const mint& rhs) {_v -= rhs._v;if (_v >= umod()) _v += umod();return *this;}constexpr mint& operator*=(const mint& rhs) {unsigned long long z = _v;z *= rhs._v;_v = (uint)(z % umod());return *this;}constexpr mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }constexpr mint operator+() const { return *this; }constexpr mint operator-() const { return mint() - *this; }constexpr mint pow(long long n) const {assert(0 <= n);mint x = *this, r = 1;while (n) {if (n & 1) r *= x;x *= x;n >>= 1;}return r;}constexpr mint inv() const {if (prime) {assert(_v);return pow(umod() - 2);} else {auto eg = inv_gcd(_v, m);assert(eg.first == 1);return eg.second;}}friend constexpr mint operator+(const mint& lhs, const mint& rhs) {return mint(lhs) += rhs;}friend constexpr mint operator-(const mint& lhs, const mint& rhs) {return mint(lhs) -= rhs;}friend constexpr mint operator*(const mint& lhs, const mint& rhs) {return mint(lhs) *= rhs;}friend constexpr mint operator/(const mint& lhs, const mint& rhs) {return mint(lhs) /= rhs;}friend constexpr bool operator==(const mint& lhs, const mint& rhs) {return lhs._v == rhs._v;}friend constexpr bool operator!=(const mint& lhs, const mint& rhs) {return lhs._v != rhs._v;}friend std::ostream &operator<<(std::ostream &os, const mint& p) {return os << p.val();}friend std::istream &operator>>(std::istream &is, mint &a) {long long t; is >> t;a = mint(t);return (is);}private:unsigned int _v;static constexpr unsigned int umod() { return m; }static constexpr bool prime = is_prime_flag<m>;};template <int id> struct dynamic_modint {using mint = dynamic_modint;public:static int mod() { return (int)(bt.umod()); }static void set_mod(int m) {assert(1 <= m);bt = barrett(m);}static mint raw(int v) {mint x;x._v = v;return x;}dynamic_modint() : _v(0) {}template<std::signed_integral T>dynamic_modint(T v){long long x = (long long)(v % (long long)(umod()));if (x < 0) x += umod();_v = (unsigned int)(x);}template<std::unsigned_integral T>dynamic_modint(T v){_v = (unsigned int)(v % umod());}uint val() const { return _v; }mint& operator++() {_v++;if (_v == umod()) _v = 0;return *this;}mint& operator--() {if (_v == 0) _v = umod();_v--;return *this;}mint operator++(int) {mint result = *this;++*this;return result;}mint operator--(int) {mint result = *this;--*this;return result;}mint& operator+=(const mint& rhs) {_v += rhs._v;if (_v >= umod()) _v -= umod();return *this;}mint& operator-=(const mint& rhs) {_v += mod() - rhs._v;if (_v >= umod()) _v -= umod();return *this;}mint& operator*=(const mint& rhs) {_v = bt.mul(_v, rhs._v);return *this;}mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }mint operator+() const { return *this; }mint operator-() const { return mint() - *this; }mint pow(long long n) const {assert(0 <= n);mint x = *this, r = 1;while (n) {if (n & 1) r *= x;x *= x;n >>= 1;}return r;}mint inv() const {auto eg = noya2::inv_gcd(_v, mod());assert(eg.first == 1);return eg.second;}friend mint operator+(const mint& lhs, const mint& rhs) {return mint(lhs) += rhs;}friend mint operator-(const mint& lhs, const mint& rhs) {return mint(lhs) -= rhs;}friend mint operator*(const mint& lhs, const mint& rhs) {return mint(lhs) *= rhs;}friend mint operator/(const mint& lhs, const mint& rhs) {return mint(lhs) /= rhs;}friend bool operator==(const mint& lhs, const mint& rhs) {return lhs._v == rhs._v;}friend bool operator!=(const mint& lhs, const mint& rhs) {return lhs._v != rhs._v;}friend std::ostream &operator<<(std::ostream &os, const mint& p) {return os << p.val();}friend std::istream &operator>>(std::istream &is, mint &a) {long long t; is >> t;a = mint(t);return (is);}private:unsigned int _v;static barrett bt;static unsigned int umod() { return bt.umod(); }};template <int id> noya2::barrett dynamic_modint<id>::bt(998244353);using modint998244353 = static_modint<998244353>;using modint1000000007 = static_modint<1000000007>;using modint = dynamic_modint<-1>;template<typename T>concept Modint = requires (T &a){T::mod();a.inv();a.val();a.pow(declval<int>());};} // namespace noya2#line 4 "/Users/noya2/Desktop/Noya2_library/fps998244353/fps998244353.hpp"#line 2 "/Users/noya2/Desktop/Noya2_library/fps998244353/ntt998244353.hpp"#line 2 "/Users/noya2/Desktop/Noya2_library/fps998244353/modint998244353.hpp"#line 4 "/Users/noya2/Desktop/Noya2_library/fps998244353/modint998244353.hpp"#line 6 "/Users/noya2/Desktop/Noya2_library/fps998244353/modint998244353.hpp"namespace noya2 {template <>struct static_modint<998244353> {using mint = static_modint;public:static constexpr int mod() { return 998244353; }static mint raw(int v) {mint x;x._v = v;return x;}constexpr static_modint() : _v(0) {}template<std::signed_integral T>constexpr static_modint(T v){long long x = (long long)(v % (long long)(umod()));if (x < 0) x += umod();_v = (unsigned int)(x);}template<std::unsigned_integral T>constexpr static_modint(T v){_v = (unsigned int)(v % umod());}constexpr unsigned int val() const { return _v; }mint& operator++() {_v++;if (_v == umod()) _v = 0;return *this;}mint& operator--() {if (_v == 0) _v = umod();_v--;return *this;}mint operator++(int) {mint result = *this;++*this;return result;}mint operator--(int) {mint result = *this;--*this;return result;}constexpr mint& operator+=(const mint& rhs) {_v += rhs._v;if (_v >= umod()) _v -= umod();return *this;}constexpr mint& operator-=(const mint& rhs) {_v -= rhs._v;if (_v >= umod()) _v += umod();return *this;}constexpr mint& operator*=(const mint& rhs) {unsigned long long z = _v;z *= rhs._v;_v = (unsigned int)(z % umod());return *this;}constexpr mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }constexpr mint operator+() const { return *this; }constexpr mint operator-() const { return mint() - *this; }constexpr mint pow(long long n) const {assert(0 <= n);mint x = *this, r = 1;while (n) {if (n & 1) r *= x;x *= x;n >>= 1;}return r;}constexpr mint inv() const {assert(_v);return pow(umod() - 2);}friend constexpr mint operator+(const mint& lhs, const mint& rhs) {return mint(lhs) += rhs;}friend constexpr mint operator-(const mint& lhs, const mint& rhs) {return mint(lhs) -= rhs;}friend constexpr mint operator*(const mint& lhs, const mint& rhs) {return mint(lhs) *= rhs;}friend constexpr mint operator/(const mint& lhs, const mint& rhs) {return mint(lhs) /= rhs;}friend constexpr bool operator==(const mint& lhs, const mint& rhs) {return lhs._v == rhs._v;}friend constexpr bool operator!=(const mint& lhs, const mint& rhs) {return lhs._v != rhs._v;}friend std::ostream &operator<<(std::ostream &os, const mint& p) {return os << p.val();}friend std::istream &operator>>(std::istream &is, mint &a) {long long t; is >> t;a = mint(t);return (is);}unsigned int _v;static constexpr int primitive_root_constexpr_v = 3;private:static constexpr unsigned int umod() { return 998244353u; }static constexpr bool prime = true;};} // namespace noya2#line 4 "/Users/noya2/Desktop/Noya2_library/fps998244353/ntt998244353.hpp"#line 7 "/Users/noya2/Desktop/Noya2_library/fps998244353/ntt998244353.hpp"namespace noya2 {namespace internal {constexpr int FFT_MAX = 23;constexpr unsigned FFT_ROOTS[FFT_MAX + 1] = {1U, 998244352U, 911660635U, 372528824U, 929031873U, 452798380U, 922799308U, 781712469U, 476477967U,166035806U, 258648936U, 584193783U, 63912897U, 350007156U, 666702199U, 968855178U, 629671588U, 24514907U, 996173970U, 363395222U, 565042129U,733596141U, 267099868U, 15311432U};constexpr unsigned INV_FFT_ROOTS[FFT_MAX + 1] = {1U, 998244352U, 86583718U, 509520358U, 337190230U, 87557064U, 609441965U, 135236158U, 304459705U,685443576U, 381598368U, 335559352U, 129292727U, 358024708U, 814576206U, 708402881U, 283043518U, 3707709U, 121392023U, 704923114U, 950391366U,428961804U, 382752275U, 469870224U};constexpr unsigned FFT_RATIOS[FFT_MAX] = {911660635U, 509520358U, 369330050U, 332049552U, 983190778U, 123842337U, 238493703U, 975955924U, 603855026U, 856644456U, 131300601U, 842657263U, 730768835U, 942482514U, 806263778U, 151565301U, 510815449U, 503497456U, 743006876U, 741047443U, 56250497U,867605899U};constexpr unsigned INV_FFT_RATIOS[FFT_MAX] = {86583718U, 372528824U, 373294451U, 645684063U, 112220581U, 692852209U, 155456985U, 797128860U,90816748U, 860285882U, 927414960U, 354738543U, 109331171U, 293255632U, 535113200U, 308540755U, 121186627U, 608385704U, 438932459U, 359477183U,824071951U, 103369235U};} // namespace noya2::internalstruct ntt998244353 {using mint = modint998244353;static constexpr unsigned MO = modint998244353::mod();static constexpr unsigned MO2 = MO * 2;static void ntt(mint *as, int n){int m = n;if (m >>= 1){for (int i = 0; i < m; i++){const unsigned x = as[i + m]._v;as[i + m]._v = as[i]._v + MO - x;as[i]._v += x;}}if (m >>= 1){mint prod = 1;for (int h = 0, i0 = 0; i0 < n; i0 += (m << 1)){for (int i = i0; i < i0 + m; i++){const unsigned x = (prod * as[i + m])._v;as[i + m]._v = as[i]._v + MO - x;as[i]._v += x;}prod *= mint::raw(internal::FFT_RATIOS[__builtin_ctz(++h)]);}}for (; m; ){if (m >>= 1){mint prod = 1;for (int h = 0, i0 = 0; i0 < n; i0 += (m << 1)){for (int i = i0; i < i0 + m; i++){const unsigned x = (prod * as[i + m])._v;as[i + m]._v = as[i]._v + MO - x;as[i]._v += x;}prod *= mint::raw(internal::FFT_RATIOS[__builtin_ctz(++h)]);}}if (m >>= 1){mint prod = 1;for (int h = 0, i0 = 0; i0 < n; i0 += (m << 1)){for (int i = i0; i < i0 + m; i++){const unsigned x = (prod * as[i + m])._v;as[i]._v = (as[i]._v >= MO2 ? as[i]._v - MO2 : as[i]._v);as[i + m]._v = as[i]._v + MO - x;as[i]._v += x;}prod *= mint::raw(internal::FFT_RATIOS[__builtin_ctz(++h)]);}}}for (int i = 0; i < n; i++){as[i]._v = (as[i]._v >= MO2 ? as[i]._v - MO2 : as[i]._v);as[i]._v = (as[i]._v >= MO ? as[i]._v - MO : as[i]._v);}}static void intt(mint *as, int n){int m = 1;if (m < (n >> 1)){mint prod = 1;for (int h = 0, i0 = 0; i0 < n; i0 += (m << 1)){for (int i = i0; i < i0 + m; i++){const unsigned long long y = as[i]._v + MO - as[i + m]._v;as[i]._v += as[i + m]._v;as[i + m]._v = prod._v * y % MO;}prod *= mint::raw(internal::INV_FFT_RATIOS[__builtin_ctz(++h)]);}m <<= 1;}for (; m < (n >> 1); m <<= 1){mint prod = 1;for (int h = 0, i0 = 0; i0 < n; i0 += (m << 1)){for (int i = i0; i < i0 + (m >> 1); i++){const unsigned long long y = as[i]._v + MO2 - as[i + m]._v;as[i]._v += as[i + m]._v;as[i]._v = (as[i]._v >= MO2 ? as[i]._v - MO2 : as[i]._v);as[i + m]._v = prod._v * y % MO;}for (int i = i0 + (m >> 1); i < i0 + m; i++){const unsigned long long y = as[i]._v + MO - as[i + m]._v;as[i]._v += as[i + m]._v;as[i + m]._v = prod._v * y % MO;}prod *= mint::raw(internal::INV_FFT_RATIOS[__builtin_ctz(++h)]);}}if (m < n){for (int i = 0; i < m; i++){const unsigned y = as[i]._v + MO2 - as[i + m]._v;as[i]._v += as[i + m]._v;as[i + m]._v = y;}}for (int i = 0; i < n; i++){as[i]._v = (as[i]._v >= MO2 ? as[i]._v - MO2 : as[i]._v);as[i]._v = (as[i]._v >= MO ? as[i]._v - MO : as[i]._v);}}static void ntt(std::vector<mint> &as){ntt(as.data(), as.size());}static void intt(std::vector<mint> &as){intt(as.data(), as.size());}static void intt_div(std::vector<mint> &as){intt(as);int n = as.size();const mint inv_n = mint::raw(n).inv();for (int i = 0; i < n; i++){as[i] *= inv_n;}}static std::vector<mint> multiply(std::vector<mint> as, std::vector<mint> bs){if (as.empty() || bs.empty()) return {};const int len = as.size() + bs.size() - 1u;if (std::min(as.size(), bs.size()) <= 40u){std::vector<mint> s(len);for (int i = 0; i < (int)(as.size()); i++){for (int j = 0; j < (int)(bs.size()); j++){s[i + j] += as[i] * bs[j];}}return s;}int n = 1;for (; n < len; n <<= 1) {}if (as.size() == bs.size() && as == bs){as.resize(n);ntt(as);for (int i = 0; i < n; i++){as[i] *= as[i];}}else {as.resize(n);ntt(as);bs.resize(n);ntt(bs);for (int i = 0; i < n; i++){as[i] *= bs[i];}}intt_div(as);as.resize(len);return as;}static void ntt_doubling(std::vector<mint> &as){auto bs = as;intt(bs);mint e = mint::raw(internal::FFT_ROOTS[std::countr_zero(as.size()) + 1]);mint iv = mint::raw(as.size()).inv();for (auto &x : bs){x *= iv;iv *= e;}ntt(bs);as.insert(as.end(), bs.begin(), bs.end());}static void ntt_pick_parity(std::vector<mint> &f, int odd){int n = f.size() / 2;mint i2 = mint::raw((mint::mod() + 1) >> 1);if (odd == 0){for (int i = 0; i < n; i++){f[i] = (f[i * 2] + f[i * 2 + 1]) * i2;}f.resize(n);return ;}mint ie = mint::raw(internal::INV_FFT_ROOTS[std::countr_zero(f.size())]);std::vector<mint> es = {i2};while ((int)(es.size()) != n){std::vector<mint> nes(es.size() * 2u);for (int i = 0; i < (int)(es.size()); i++){nes[i * 2 + 0] = es[i];nes[i * 2 + 1] = es[i] * ie;}ie *= ie;std::swap(es, nes);}for (int i = 0; i < n; i++){f[i] = (f[i * 2] - f[i * 2 + 1]) * es[i];}f.resize(n);}};} // namespace noya2#line 2 "/Users/noya2/Desktop/Noya2_library/math/binomial.hpp"#line 4 "/Users/noya2/Desktop/Noya2_library/math/binomial.hpp"namespace noya2 {template<typename mint>struct binomial {binomial(int len = 300000){ extend(len); }static mint fact(int n){if (n < 0) return 0;while (n >= (int)_fact.size()) extend();return _fact[n];}static mint ifact(int n){if (n < 0) return 0;while (n >= (int)_fact.size()) extend();return _ifact[n];}static mint inv(int n){return ifact(n) * fact(n-1);}static mint C(int n, int r){if (!(0 <= r && r <= n)) return 0;return fact(n) * ifact(r) * ifact(n-r);}static mint P(int n, int r){if (!(0 <= r && r <= n)) return 0;return fact(n) * ifact(n-r);}inline mint operator()(int n, int r) { return C(n, r); }template<class... Cnts>static mint M(const Cnts&... cnts){return multinomial(0,1,cnts...);}static void initialize(int len = 2){_fact.clear();_ifact.clear();extend(len);}private:static mint multinomial(const int& sum, const mint& div_prod){if (sum < 0) return 0;return fact(sum) * div_prod;}template<class... Tail>static mint multinomial(const int& sum, const mint& div_prod, const int& n1, const Tail&... tail){if (n1 < 0) return 0;return multinomial(sum+n1,div_prod*ifact(n1),tail...);}static inline std::vector<mint> _fact, _ifact;static void extend(int len = -1){if (_fact.empty()){_fact = _ifact = {1,1};}int siz = _fact.size();if (len == -1) len = siz * 2;len = (int)min<long long>(len, mint::mod() - 1);if (len < siz) return ;_fact.resize(len+1), _ifact.resize(len+1);for (int i = siz; i <= len; i++) _fact[i] = _fact[i-1] * i;_ifact[len] = _fact[len].inv();for (int i = len; i > siz; i--) _ifact[i-1] = _ifact[i] * i;}};} // namespace noya2#line 7 "/Users/noya2/Desktop/Noya2_library/fps998244353/fps998244353.hpp"namespace noya2 {// Formal Power Series for modint998244353struct fps998244353 : std::vector<modint998244353> {using mint = modint998244353;using std::vector<mint>::vector;using std::vector<mint>::operator=;using fps = fps998244353;static inline binomial<mint> bnm;fps998244353 (const std::vector<mint> &init){(*this) = init;}void shrink(){while(!(this->empty()) && this->back().val() == 0){this->pop_back();}}fps &operator*= (const mint &r){for (auto &x : *this) x *= r;return *this;}fps &operator/= (const mint &r){(*this) *= r.inv();return *this;}fps &operator<<= (const int &d){this->insert(this->begin(), d, mint(0));return *this;}fps &operator>>= (const int &d){if ((int)(this->size()) <= d) this->clear();else this->erase(this->begin(),this->begin() + d);return *this;}fps &operator+= (const fps &r){if (this->size() < r.size()) this->resize(r.size());for (int i = 0; auto x : r){(*this)[i++] += x;}return *this;}fps &operator-= (const fps &r){if (this->size() < r.size()) this->resize(r.size());for (int i = 0; auto x : r){(*this)[i++] -= x;}return *this;}fps &operator*= (const fps &r){if (this->empty() || r.empty()){this->clear();return *this;}(*this) = ntt998244353::multiply(*this, r);return *this;}fps operator* (const mint &r) const { return fps(*this) *= r; }fps operator/ (const mint &r) const { return fps(*this) /= r; }fps operator<< (const int &d) const { return fps(*this) <<= d; }fps operator>> (const int &d) const { return fps(*this) >>= d; }fps operator+ (const fps &r) const { return fps(*this) += r; }fps operator- (const fps &r) const { return fps(*this) -= r; }fps operator* (const fps &r) const { return fps(*this) *= r; }fps operator+ () const { return *this; }fps operator- () const {fps ret(*this);for (auto &x : ret) x = -x;return ret;}mint eval(const mint &x) const {mint res(0), w(1);for (auto a : *this){res += a * w;w *= x;}return res;}[[nodiscard("Do not change but return changed object.")]]fps pre(std::size_t sz) const {fps ret(this->begin(), this->begin() + std::min(this->size(), sz));if (ret.size() < sz) ret.resize(sz);return ret;}[[nodiscard("Do not change but return changed object.")]]fps rev() const {fps ret(*this);std::reverse(ret.begin(), ret.end());return ret;}[[nodiscard("Do not change but return changed object.")]]fps diff() const {if (this->empty()){return fps();}fps ret(this->begin() + 1, this->end());for (int i = 1; auto &x : ret){x *= i++;}return ret;}[[nodiscard("Do not change but return changed object.")]]fps integral() const {if (this->empty()){return fps();}fps ret(1, mint(0));ret.insert(ret.end(), this->begin(), this->end());for (int i = 0; auto &x : ret){x *= bnm.inv(i++); // inv(0) = 0}return ret;}[[nodiscard("Do not change but return changed object.")]]fps inv(int d = -1) const {const int n = this->size();if (d == -1) d = n;fps res = {(*this)[0].inv()};for (int siz = 1; siz < d; siz <<= 1){fps f(this->begin(),this->begin()+min(n,siz*2)), g(res);f.resize(siz*2), g.resize(siz*2);f.ntt(), g.ntt();for (int i = 0; i < siz*2; i++) f[i] *= g[i];f.intt();f.erase(f.begin(),f.begin()+siz);f.resize(siz*2);f.ntt();for (int i = 0; i < siz*2; i++) f[i] *= g[i];f.intt();mint siz2_inv = mint(siz*2).inv(); siz2_inv *= -siz2_inv;for (int i = 0; i < siz; i++) f[i] *= siz2_inv;res.insert(res.end(),f.begin(),f.begin()+siz);}res.resize(d);return res;}[[nodiscard("Do not change but return changed object.")]]fps log(int d = -1) const {assert(this->empty() == false && (*this)[0].val() == 1u);if (d == -1) d = this->size();return (this->diff() * this->inv(d)).pre(d - 1).integral();}[[nodiscard("Do not change but return changed object.")]]fps exp(int d = -1) const {const int n = this->size();if (d == -1) d = n;assert(n == 0 || (*this)[0].val() == 0u);if (n <= 1){fps ret(1,1);ret.resize(d);return ret;}// n >= 2fps f = {mint(1), (*this)[1]}, ret = f;for (int sz = 2; sz < d; sz <<= 1){f.insert(f.end(), this->begin()+std::min(n,sz), this->begin()+std::min(n,sz*2));f.resize(sz*2);ret *= f - ret.log(sz*2);ret.resize(sz*2);}ret.resize(d);return ret;}[[nodiscard("Do not change but return changed object.")]]fps pow(long long k, int d = -1) const {const int n = this->size();if (d == -1) d = n;if (k == 0){fps ret(d, mint(0));if (d >= 1) ret[0] = 1;return ret;}// Find left-most nonzero term.for (int i = 0; i < n; i++){if ((*this)[i].val() != 0u){mint iv = (*this)[i].inv();fps ret = ((((*this) * iv) >> i).log(d) * mint(k)).exp(d);ret *= (*this)[i].pow(k);ret = (ret << (i * k)).pre(d);return ret;}if ((i + 1) * k >= d) break;}return fps(d, mint(0));}void ntt(){ntt998244353::ntt(*this);}// NOT /= lenvoid intt(){ntt998244353::intt(*this);}// already /= lenvoid intt_div(){ntt998244353::intt_div(*this);}// input : ntt( f[0, 2^n) )// output : ntt( f[0, 2^n) ++ zero_padding[0, 2^n) )void ntt_doubling(){ntt998244353::ntt_doubling(*this);}// input : ntt( f[0, 2^n) )// output : ntt( g[0, 2^{n-1}) ), g[i] = f[i * 2 + odd]void ntt_pick_parity(int odd){ntt998244353::ntt_pick_parity(*this, odd);}fps quotient(fps r) const {r.shrink();const int n = this->size(), m = r.size();if (n < m){return fps();}fps quo(*this);const int sz = n - m + 1;std::reverse(quo.begin(), quo.end());std::reverse(r.begin(), r.end());quo.resize(sz);quo *= r.inv(sz);quo.resize(sz);std::reverse(quo.begin(), quo.end());return quo;}fps remainder(fps r) const {r.shrink();const int n = this->size(), m = r.size();if (n < m){return fps(*this);}fps rem(*this);rem -= quotient(r) * r;rem.resize(m-1);rem.shrink();return rem;}std::pair<fps,fps> remquo(fps r) const {r.shrink();fps quo = quotient(r);fps rem(*this);rem -= quo * r;rem.shrink();return {rem, quo};}};} // namespace noya2#line 4 "c.cpp"using mint = modint998244353;using fps = fps998244353;void solve(){binomial<mint> bnm;int n; in(n);int k; in(k);vector<int> a(n); in(a);sort(all(a));rep(i,n) chmin(a[i],k);mint ans = 0;map<int,mint> mp;fps expf(k+1);rep(i,k+1){expf[i] = bnm.ifact(i);}vector<fps> ls(k+2);for (int i = 1; i <= k+1; i++){ls[i] = expf.pre(i).log(k+1);}for (int rot = 1; rot <= k; rot++){int g = gcd(rot,k);if (mp.contains(g)){ans += mp[g];continue;}int c = k/g;fps logs = {};for (int l = 0, r = 0; l < n; l = r){while (r < n && min(a[l]/c,g) == min(a[r]/c,g)) r++;int cnt = min(a[l]/c,g) + 1;logs += ls[cnt] * (r - l);}auto prd = logs.exp(g+1);mint cur = prd[g] * bnm.fact(g);ans += cur;mp[g] = cur;}ans /= k;out(ans);}int main(){int t = 1; //in(t);while (t--) { solve(); }}