#include #include #pragma GCC target("avx2") #pragma GCC optimize("O3") #pragma GCC optimize("unroll-loops") #define FOR1(a) for (ll _ = 0; _ < ll(a); ++_) #define FOR2(i, a) for (ll i = 0; i < ll(a); ++i) #define FOR3(i, a, b) for (ll i = a; i < ll(b); ++i) #define FOR4(i, a, b, c) for (ll i = a; i < ll(b); i += (c)) #define FOR1_R(a) for (ll i = (a)-1; i >= ll(0); --i) #define FOR2_R(i, a) for (ll i = (a)-1; i >= ll(0); --i) #define FOR3_R(i, a, b) for (ll i = (b)-1; i >= ll(a); --i) #define overload4(a, b, c, d, e, ...) e #define overload3(a, b, c, d, ...) d #define FOR(...) overload4(__VA_ARGS__, FOR4, FOR3, FOR2, FOR1)(__VA_ARGS__) #define FOR_R(...) overload3(__VA_ARGS__, FOR3_R, FOR2_R, FOR1_R)(__VA_ARGS__) #define sz(c) ((int)(c).size()) #define ten(x) ((int)1e##x) #define all(v) (v).begin(), (v).end() using namespace std; using ll=long long; using P = pair; const long double PI=acos(-1); const ll INF=1e18; const int inf=1e9; template< uint32_t mod, bool fast = false > struct MontgomeryModInt { using mint = MontgomeryModInt; using i32 = int32_t; using i64 = int64_t; using u32 = uint32_t; using u64 = uint64_t; static constexpr u32 get_r() { u32 ret = mod; for(i32 i = 0; i < 4; i++) ret *= 2 - mod * ret; return ret; } static constexpr u32 r = get_r(); static constexpr u32 n2 = -u64(mod) % mod; static_assert(r * mod == 1, "invalid, r * mod != 1"); static_assert(mod < (1 << 30), "invalid, mod >= 2 ^ 30"); static_assert((mod & 1) == 1, "invalid, mod % 2 == 0"); u32 a; MontgomeryModInt() : a{} {} MontgomeryModInt(const i64 &x) : a(reduce(u64(fast ? x : (x % mod + mod)) * n2)) {} static constexpr u32 reduce(const u64 &b) { return u32(b >> 32) + mod - u32((u64(u32(b) * r) * mod) >> 32); } constexpr mint& operator+=(const mint &p) { if(i32(a += p.a - 2 * mod) < 0) a += 2 * mod; return *this; } constexpr mint& operator-=(const mint &p) { if(i32(a -= p.a) < 0) a += 2 * mod; return *this; } constexpr mint& operator*=(const mint &p) { a = reduce(u64(a) * p.a); return *this; } constexpr mint& operator/=(const mint &p) { *this *= modinv(p); return *this; } constexpr mint operator-() const { return mint() - *this; } constexpr mint operator+(const mint &p) const { return mint(*this) += p; } constexpr mint operator-(const mint &p) const { return mint(*this) -= p; } constexpr mint operator*(const mint &p) const { return mint(*this) *= p; } constexpr mint operator/(const mint &p) const { return mint(*this) /= p; } constexpr bool operator==(const mint &p) const { return (a >= mod ? a - mod : a) == (p.a >= mod ? p.a - mod : p.a); } constexpr bool operator!=(const mint &p) const { return (a >= mod ? a - mod : a) != (p.a >= mod ? p.a - mod : p.a); } u32 get() const { u32 ret = reduce(a); return ret >= mod ? ret - mod : ret; } friend constexpr MontgomeryModInt modpow(const MontgomeryModInt &x,u64 n) noexcept { MontgomeryModInt ret(1), mul(x); while(n > 0) { if(n & 1) ret *= mul; mul *= mul; n >>= 1; } return ret; } friend constexpr MontgomeryModInt modinv(const MontgomeryModInt &r) noexcept { u64 a = r.get(), b = mod, u = 1, v = 0; while (b) { long long t = a / b; a -= t * b, swap(a, b); u -= t * v, swap(u, v); } return MontgomeryModInt(u); } friend ostream &operator<<(ostream &os, const mint &p) { return os << p.get(); } friend istream &operator>>(istream &is, mint &a) { i64 t; is >> t; a = mint(t); return is; } static constexpr u32 getmod() { return mod; } }; ll modpow(ll a,ll n,ll mod){ ll res=1; a%=mod; while (n>0){ if (n & 1) res*=a; a *= a; a%=mod; n >>= 1; res%=mod; } return res; } template< typename T > struct Combination { vector< T > _fact, _rfact, _inv; Combination(int sz) : _fact(sz + 1), _rfact(sz + 1), _inv(sz + 1) { _fact[0] = _rfact[sz] = _inv[0] = 1; for(int i = 1; i <= sz; i++) _fact[i] = _fact[i - 1] * i; _rfact[sz] /= _fact[sz]; for(int i = sz - 1; i >= 0; i--) _rfact[i] = _rfact[i + 1] * (i + 1); for(int i = 1; i <= sz; i++) _inv[i] = _rfact[i] * _fact[i - 1]; } inline T fact(int k) const { return _fact[k]; } inline T rfact(int k) const { return _rfact[k]; } inline T inv(int k) const { return _inv[k]; } T P(int n, int r) const { if(r < 0 || n < r) return 0; return fact(n) * rfact(n - r); } T C(int p, int q) const { if(q < 0 || p < q) return 0; return fact(p) * rfact(q) * rfact(p - q); } T H(int n, int r) const { if(n < 0 || r < 0) return (0); return r == 0 ? 1 : C(n + r - 1, r); } }; //fast Input by yosupo #include #include #include #include #include #include #include #include #include #include namespace fastio{ /* quote from yosupo's submission in Library Checker */ int bsr(unsigned int n) { return 8 * (int)sizeof(unsigned int) - 1 - __builtin_clz(n); } // @param n `1 <= n` // @return maximum non-negative `x` s.t. `(n & (1 << x)) != 0` int bsr(unsigned long n) { return 8 * (int)sizeof(unsigned long) - 1 - __builtin_clzl(n); } // @param n `1 <= n` // @return maximum non-negative `x` s.t. `(n & (1 << x)) != 0` int bsr(unsigned long long n) { return 8 * (int)sizeof(unsigned long long) - 1 - __builtin_clzll(n); } // @param n `1 <= n` // @return minimum non-negative `x` s.t. `(n & (1 << x)) != 0` int bsr(unsigned __int128 n) { unsigned long long low = (unsigned long long)(n); unsigned long long high = (unsigned long long)(n >> 64); return high ? 127 - __builtin_clzll(high) : 63 - __builtin_ctzll(low); } namespace internal { template using is_signed_int128 = typename std::conditional::value || std::is_same::value, std::true_type, std::false_type>::type; template using is_unsigned_int128 = typename std::conditional::value || std::is_same::value, std::true_type, std::false_type>::type; template using make_unsigned_int128 = typename std::conditional::value, __uint128_t, unsigned __int128>; template using is_integral = typename std::conditional::value || internal::is_signed_int128::value || internal::is_unsigned_int128::value, std::true_type, std::false_type>::type; template using is_signed_int = typename std::conditional<(is_integral::value && std::is_signed::value) || is_signed_int128::value, std::true_type, std::false_type>::type; template using is_unsigned_int = typename std::conditional<(is_integral::value && std::is_unsigned::value) || is_unsigned_int128::value, std::true_type, std::false_type>::type; template using to_unsigned = typename std::conditional< is_signed_int128::value, make_unsigned_int128, typename std::conditional::value, std::make_unsigned, std::common_type>::type>::type; template using is_integral_t = std::enable_if_t::value>; template using is_signed_int_t = std::enable_if_t::value>; template using is_unsigned_int_t = std::enable_if_t::value>; template using to_unsigned_t = typename to_unsigned::type; } // namespace internal struct Scanner { public: Scanner(const Scanner&) = delete; Scanner& operator=(const Scanner&) = delete; Scanner(FILE* fp) : fd(fileno(fp)) {} void read() {} template void read(H& h, T&... t) { bool f = read_single(h); assert(f); read(t...); } int read_unsafe() { return 0; } template int read_unsafe(H& h, T&... t) { bool f = read_single(h); if (!f) return 0; return 1 + read_unsafe(t...); } int close() { return ::close(fd); } private: static constexpr int SIZE = 1 << 15; int fd = -1; std::array line; int st = 0, ed = 0; bool eof = false; bool read_single(std::string& ref) { if (!skip_space()) return false; ref = ""; while (true) { char c = top(); if (c <= ' ') break; ref += c; st++; } return true; } bool read_single(double& ref) { std::string s; if (!read_single(s)) return false; ref = std::stod(s); return true; } template ::value>* = nullptr> bool read_single(T& ref) { if (!skip_space<50>()) return false; ref = top(); st++; return true; } template * = nullptr, std::enable_if_t::value>* = nullptr> bool read_single(T& sref) { using U = internal::to_unsigned_t; if (!skip_space<50>()) return false; bool neg = false; if (line[st] == '-') { neg = true; st++; } U ref = 0; do { ref = 10 * ref + (line[st++] & 0x0f); } while (line[st] >= '0'); sref = neg ? -ref : ref; return true; } template * = nullptr, std::enable_if_t::value>* = nullptr> bool read_single(U& ref) { if (!skip_space<50>()) return false; ref = 0; do { ref = 10 * ref + (line[st++] & 0x0f); } while (line[st] >= '0'); return true; } bool reread() { if (ed - st >= 50) return true; if (st > SIZE / 2) { std::memmove(line.data(), line.data() + st, ed - st); ed -= st; st = 0; } if (eof) return false; auto u = ::read(fd, line.data() + ed, SIZE - ed); if (u == 0) { eof = true; line[ed] = '\0'; u = 1; } ed += int(u); line[ed] = char(127); return true; } char top() { if (st == ed) { bool f = reread(); assert(f); } return line[st]; } template bool skip_space() { while (true) { while (line[st] <= ' ') st++; if (ed - st > TOKEN_LEN) return true; if (st > ed) st = ed; for (auto i = st; i < ed; i++) { if (line[i] <= ' ') return true; } if (!reread()) return false; } } }; //fast Output by ei1333 /** * @brief Printer(高速出力) */ struct Printer { public: explicit Printer(FILE *fp) : fp(fp) {} ~Printer() { flush(); } template< bool f = false, typename T, typename... E > void write(const T &t, const E &... e) { if(f) write_single(' '); write_single(t); write< true >(e...); } template< typename... T > void writeln(const T &...t) { write(t...); write_single('\n'); } void flush() { fwrite(line, 1, st - line, fp); st = line; } private: FILE *fp = nullptr; static constexpr size_t line_size = 1 << 16; static constexpr size_t int_digits = 20; char line[line_size + 1] = {}; char small[32] = {}; char *st = line; template< bool f = false > void write() {} void write_single(const char &t) { if(st + 1 >= line + line_size) flush(); *st++ = t; } template< typename T, enable_if_t< is_integral< T >::value, int > = 0 > void write_single(T s) { if(st + int_digits >= line + line_size) flush(); if(s == 0) { write_single('0'); return; } if(s < 0) { write_single('-'); s = -s; } char *mp = small + sizeof(small); typename make_unsigned< T >::type y = s; size_t len = 0; while(y > 0) { *--mp = y % 10 + '0'; y /= 10; ++len; } memmove(st, mp, len); st += len; } void write_single(const string &s) { for(auto &c : s) write_single(c); } void write_single(const char *s) { while(*s != 0) write_single(*s++); } template< typename T > void write_single(const vector< T > &s) { for(size_t i = 0; i < s.size(); i++) { if(i) write_single(' '); write_single(s[i]); } } }; }; //namespace fastio struct dynamic_Fp{ static int &mod(){ static int mod_=0; return mod_; } ll val; static void set_mod(int m){ mod() = m; } static int getmod() { return mod(); } dynamic_Fp(long long v = 0) noexcept : val(v % getmod()) { if (val < 0) val += getmod(); } dynamic_Fp operator - () const noexcept { return val ? getmod() - val : 0; } dynamic_Fp operator + (const dynamic_Fp& r) const noexcept { return dynamic_Fp(*this) += r; } dynamic_Fp operator - (const dynamic_Fp& r) const noexcept { return dynamic_Fp(*this) -= r; } dynamic_Fp operator * (const dynamic_Fp& r) const noexcept { return dynamic_Fp(*this) *= r; } dynamic_Fp operator / (const dynamic_Fp& r) const noexcept { return dynamic_Fp(*this) /= r; } dynamic_Fp& operator += (const dynamic_Fp& r) noexcept { val += r.val; if (val >= getmod()) val -= getmod(); return *this; } dynamic_Fp& operator -= (const dynamic_Fp& r) noexcept { val -= r.val; if (val < 0) val += getmod(); return *this; } dynamic_Fp& operator *= (const dynamic_Fp& r) noexcept { val = val * r.val % getmod(); return *this; } dynamic_Fp& operator /= (const dynamic_Fp& r) noexcept { ll a = r.val, b = getmod(), u = 1, v = 0; while (b) { ll t = a / b; a -= t * b, swap(a, b); u -= t * v, swap(u, v); } val = val * u % getmod(); if (val < 0) val += getmod(); return *this; } bool operator == (const dynamic_Fp& r) const noexcept { return this->val == r.val; } bool operator != (const dynamic_Fp& r) const noexcept { return this->val != r.val; } bool operator < (const dynamic_Fp& r) const noexcept { return this->val < r.val; } friend istream& operator >> (istream& is, dynamic_Fp& x) noexcept { is >> x.val; x.val %= getmod(); if (x.val < 0) x.val += getmod(); return is; } friend ostream& operator << (ostream& os, const dynamic_Fp& x) noexcept { return os << x.val; } friend dynamic_Fp modpow(const dynamic_Fp& a, long long n) noexcept { dynamic_Fp res=1,r=a; while(n){ if(n&1) res*=r; r*=r; n>>=1; } return res; } friend dynamic_Fp modinv(const dynamic_Fp& r) noexcept { long long a = r.val, b = getmod(), u = 1, v = 0; while (b) { long long t = a / b; a -= t * b, swap(a, b); u -= t * v, swap(u, v); } return dynamic_Fp(u); } }; using mint=MontgomeryModInt<998244353>; int main(){ fastio::Scanner sc(stdin); fastio::Printer pr(stdout); #define in(...) sc.read(__VA_ARGS__) #define LL(...) ll __VA_ARGS__;in(__VA_ARGS__) #define INT(...) int __VA_ARGS__;in(__VA_ARGS__) #define STR(...) string __VA_ARGS__;in(__VA_ARGS__) #define out(...) pr.write(__VA_ARGS__) #define outln(...) pr.writeln(__VA_ARGS__) #define outspace(...) pr.write(__VA_ARGS__),pr.write(' ') #define rall(v) (v).rbegin(), (v).rend() #define fi first #define se second /* */ using Mint=dynamic_Fp; INT(n,m); Mint::set_mod(m); // dp[i][j][k] := i-i+2のやり方、最後が下につなげたやつかどうか、分断した回数+下に引いた回数mod2 vector> dp(2,vector(2)); dp[0][0]=1; Mint ans=1; FOR(i,1,n*2-2){ vector> ndp(2,vector(2)); ndp[0][0]=dp[0][0]+dp[0][1]*Mint(i-1)*Mint(i)+dp[1][1]*Mint(i); ndp[0][1]=dp[0][1]+dp[1][1]; ndp[1][1]=dp[0][0]+dp[0][1]*Mint(i-1)+dp[1][1]; swap(dp,ndp); if(i&1) ans*=dp[0][1]+dp[1][1]; } FOR(i,1,n*2) ans*=i; outln(ans.val); }