#pragma GCC optimize("O3,unroll-loops") #pragma GCC target("avx2,bmi,bmi2,lzcnt,popcnt") #include #include using namespace std; using namespace atcoder; typedef long long int ll; typedef long double ld; typedef vector vi; typedef vector vvi; typedef vector vvvi; typedef vector vvvvi; typedef vector vl; typedef vector vvl; typedef vector vvvl; typedef vector vvvvl; typedef vector vb; typedef vector vvb; typedef vector vvvb; typedef vector vvvvb; typedef pair pl; typedef pair ppl; typedef pair pppl; typedef pair pppppl; #define endl '\n' #define pb push_back #define eb emplace_back #define rep(i,a,b) for(int i=(a);i<(b);i++) #define rrep(i,a,b) for(int i=(b)-1;i>=(a);i--) #define all(a) begin(a),end(a) #define rall(a) rbegin(a),rend(a) #define sz(a) (int)(a).size() #define F first #define S second #define bs(A,x) binary_search(all(A),x) #define lb(A,x) (ll)(lower_bound(all(A),x)-A.begin()) #define ub(A,x) (ll)(upper_bound(all(A),x)-A.begin()) #define cou(A,x) (ll)(upper_bound(all(A),x)-lower_bound(all(A),x)) templateusing min_priority_queue=priority_queue,greater>; templatebool chmax(T&a,T b){if(abool chmin(T&a,T b){if(bostream&operator<<(ostream&os,pairp){os<istream&operator>>(istream&is,pair&p){is>>p.F>>p.S;return is;} templateostream&operator<<(ostream&os,vectorv){rep(i,0,sz(v))os<istream&operator>>(istream&is,vector&v){for(T&in:v)is>>in;return is;} long long mfloor(long long x,long long y){ return (x/y-((x^y)<0&&(x%y))); } template struct LazyMontgomeryModInt { using mint = LazyMontgomeryModInt; using i32 = int32_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(mod < (1 << 30), "invalid, mod >= 2 ^ 30"); static_assert((mod & 1) == 1, "invalid, mod % 2 == 0"); static_assert(r * mod == 1, "this code has bugs."); u32 a; constexpr LazyMontgomeryModInt() : a(0) {} constexpr LazyMontgomeryModInt(const int64_t &b) : a(reduce(u64(b % mod + mod) * n2)){}; static constexpr u32 reduce(const u64 &b) { return (b + u64(u32(b) * u32(-r)) * mod) >> 32; } constexpr mint &operator+=(const mint &b) { if (i32(a += b.a - 2 * mod) < 0) a += 2 * mod; return *this; } constexpr mint &operator-=(const mint &b) { if (i32(a -= b.a) < 0) a += 2 * mod; return *this; } constexpr mint &operator*=(const mint &b) { a = reduce(u64(a) * b.a); return *this; } constexpr mint &operator/=(const mint &b) { *this *= b.inverse(); return *this; } constexpr mint operator+(const mint &b) const { return mint(*this) += b; } constexpr mint operator-(const mint &b) const { return mint(*this) -= b; } constexpr mint operator*(const mint &b) const { return mint(*this) *= b; } constexpr mint operator/(const mint &b) const { return mint(*this) /= b; } constexpr bool operator==(const mint &b) const { return (a >= mod ? a - mod : a) == (b.a >= mod ? b.a - mod : b.a); } constexpr bool operator!=(const mint &b) const { return (a >= mod ? a - mod : a) != (b.a >= mod ? b.a - mod : b.a); } constexpr mint operator-() const { return mint() - mint(*this); } constexpr mint operator+() const { return mint(*this); } constexpr mint pow(u64 n) const { mint ret(1), mul(*this); while (n > 0) { if (n & 1) ret *= mul; mul *= mul; n >>= 1; } return ret; } constexpr mint inverse() const { int x = get(), y = mod, u = 1, v = 0, t = 0, tmp = 0; while (y > 0) { t = x / y; x -= t * y, u -= t * v; tmp = x, x = y, y = tmp; tmp = u, u = v, v = tmp; } return mint{u}; } friend ostream &operator<<(ostream &os, const mint &b) { return os << b.get(); } friend istream &operator>>(istream &is, mint &b) { int64_t t; is >> t; b = LazyMontgomeryModInt(t); return (is); } constexpr u32 get() const { u32 ret = reduce(a); return ret >= mod ? ret - mod : ret; } static constexpr u32 get_mod() { return mod; } }; template struct Binomial { vector f, g, h; Binomial(int MAX = 0) { assert(T::get_mod() != 0 && "Binomial()"); f.resize(1, T{1}); g.resize(1, T{1}); h.resize(1, T{1}); if (MAX > 0) extend(MAX + 1); } void extend(int m = -1) { int n = f.size(); if (m == -1) m = n * 2; m = min(m, T::get_mod()); if (n >= m) return; f.resize(m); g.resize(m); h.resize(m); for (int i = n; i < m; i++) f[i] = f[i - 1] * T(i); g[m - 1] = f[m - 1].inverse(); h[m - 1] = g[m - 1] * f[m - 2]; for (int i = m - 2; i >= n; i--) { g[i] = g[i + 1] * T(i + 1); h[i] = g[i] * f[i - 1]; } } T fac(int i) { if (i < 0) return T(0); while (i >= (int)f.size()) extend(); return f[i]; } T finv(int i) { if (i < 0) return T(0); while (i >= (int)g.size()) extend(); return g[i]; } T inv(int i) { if (i < 0) return -inv(-i); while (i >= (int)h.size()) extend(); return h[i]; } T C(int n, int r) { if (n < 0 || n < r || r < 0) return T(0); return fac(n) * finv(n - r) * finv(r); } inline T operator()(int n, int r) { return C(n, r); } template T multinomial(const vector& r) { static_assert(is_integral::value == true); int n = 0; for (auto& x : r) { if (x < 0) return T(0); n += x; } T res = fac(n); for (auto& x : r) res *= finv(x); return res; } template T operator()(const vector& r) { return multinomial(r); } T C_naive(int n, int r) { if (n < 0 || n < r || r < 0) return T(0); T ret = T(1); r = min(r, n - r); for (int i = 1; i <= r; ++i) ret *= inv(i) * (n--); return ret; } T P(int n, int r) { if (n < 0 || n < r || r < 0) return T(0); return fac(n) * finv(n - r); } T H(int n, int r) { if (n < 0 || r < 0) return T(0); return r == 0 ? 1 : C(n + r - 1, r); } }; using mint = LazyMontgomeryModInt<998244353>; Binomial C; typedef vector vm; typedef vector vvm; typedef vector vvvm; typedef vector vvvvm; int main(){ cin.tie(0)->sync_with_stdio(0); cin.exceptions(cin.failbit); // int n; cin>>n; while(n--)cout<<"Hello world!"< factorize(n):重複素因数 map factor_count(n):素因数分解 vector divisors(n):約数列挙 ------------------- mint C(n,r):二項係数 mint C.P(n,r):順列 mint C.H(n,r):重複組み合わせ mint C.fac(n):階乗 mint C.finv(n):階乗逆元 mint C.inv(n):逆元 mint C.multinomial({a,b,c,...}):多項係数 ------------------- */