//#define _GLIBCXX_DEBUG //#pragma GCC target("avx2") //#pragma GCC optimize("O3") //#pragma GCC optimize("unroll-loops") #include using namespace std; #ifdef LOCAL #include #define OUT(...) debug_print::multi_print(#__VA_ARGS__, __VA_ARGS__) #else #define OUT(...) (static_cast(0)) #endif #define endl '\n' #define lfs cout<= (ll)(n); i--) using ll = long long; using ld = long double; const ll MOD1 = 1e9+7; const ll MOD9 = 998244353; const ll INF = 1e18; using P = pair; template using PQ = priority_queue; template using QP = priority_queue,greater>; templatebool chmin(T1 &a,T2 b){if(a>b){a=b;return true;}else return false;} templatebool chmax(T1 &a,T2 b){if(avoid ans(bool x,T1 y,T2 z){if(x)cout<void anss(T1 x,T2 y,T3 z){ans(x!=y,x,z);}; templatevoid debug(const T &v,ll h,ll w,string sv=" "){for(ll i=0;ivoid debug(const T &v,ll n,string sv=" "){if(n!=0)cout<void debug(const vector&v){debug(v,v.size());} templatevoid debug(const vector>&v){for(auto &vv:v)debug(vv,vv.size());} templatevoid debug(stack st){while(!st.empty()){cout<void debug(queue st){while(!st.empty()){cout<void debug(deque st){while(!st.empty()){cout<void debug(PQ st){while(!st.empty()){cout<void debug(QP st){while(!st.empty()){cout<void debug(const set&v){for(auto z:v)cout<void debug(const multiset&v){for(auto z:v)cout<void debug(const array &a){for(auto z:a)cout<void debug(const map&v){for(auto z:v)cout<<"["<vector>vec(ll x, ll y, T w){vector>v(x,vector(y,w));return v;} vectordx={1,-1,0,0,1,1,-1,-1};vectordy={0,0,1,-1,1,-1,1,-1}; templatevector make_v(size_t a,T b){return vector(a,b);} templateauto make_v(size_t a,Ts... ts){return vector(a,make_v(ts...));} templateostream &operator<<(ostream &os, const pair&p){return os << "(" << p.first << "," << p.second << ")";} templateostream &operator<<(ostream &os, const vector &v){os<<"[";for(auto &z:v)os << z << ",";os<<"]"; return os;} templatevoid rearrange(vector&ord, vector&v){ auto tmp = v; for(int i=0;ivoid rearrange(vector&ord,Head&& head, Tail&&... tail){ rearrange(ord, head); rearrange(ord, tail...); } template vector ascend(const vector&v){ vectorord(v.size());iota(ord.begin(),ord.end(),0); sort(ord.begin(),ord.end(),[&](int i,int j){return make_pair(v[i],i) vector descend(const vector&v){ vectorord(v.size());iota(ord.begin(),ord.end(),0); sort(ord.begin(),ord.end(),[&](int i,int j){return make_pair(v[i],-i)>make_pair(v[j],-j);}); return ord; } template vector inv_perm(const vector&ord){ vectorinv(ord.size()); for(int i=0;i0);return n>=0?n/div:(n-div+1)/div;} ll CEIL(ll n,ll div){assert(div>0);return n>=0?(n+div-1)/div:n/div;} ll digitsum(ll n){ll ret=0;while(n){ret+=n%10;n/=10;}return ret;} ll modulo(ll n,ll d){return (n%d+d)%d;}; templateT min(const vector&v){return *min_element(v.begin(),v.end());} templateT max(const vector&v){return *max_element(v.begin(),v.end());} templateT acc(const vector&v){return accumulate(v.begin(),v.end(),T(0));}; templateT reverse(const T &v){return T(v.rbegin(),v.rend());}; //mt19937 mt(chrono::steady_clock::now().time_since_epoch().count()); int popcount(ll x){return __builtin_popcountll(x);}; int poplow(ll x){return __builtin_ctzll(x);}; int pophigh(ll x){return 63 - __builtin_clzll(x);}; templateT poll(queue &q){auto ret=q.front();q.pop();return ret;}; templateT poll(priority_queue &q){auto ret=q.top();q.pop();return ret;}; templateT poll(QP &q){auto ret=q.top();q.pop();return ret;}; templateT poll(stack &s){auto ret=s.top();s.pop();return ret;}; ll MULT(ll x,ll y){if(LLONG_MAX/x<=y)return LLONG_MAX;return x*y;} ll POW2(ll x, ll k){ll ret=1,mul=x;while(k){if(mul==LLONG_MAX)return LLONG_MAX;if(k&1)ret=MULT(ret,mul);mul=MULT(mul,mul);k>>=1;}return ret;} ll POW(ll x, ll k){ll ret=1;for(int i=0;isputn(d, len) != len) { dest.setstate(std::ios_base::badbit); } } return dest; } namespace converter{ int dict[500]; const string lower="abcdefghijklmnopqrstuvwxyz"; const string upper="ABCDEFGHIJKLMNOPQRSTUVWXYZ"; const string digit="0123456789"; const string digit1="123456789"; void regi_str(const string &t){ for(int i=0;ito_int(const string &s,const string &t){ regi_str(t); vectorret(s.size()); for(int i=0;ito_int(const string &s){ auto t=s; sort(t.begin(),t.end()); t.erase(unique(t.begin(),t.end()),t.end()); return to_int(s,t); } vector>to_int(const vector&s,const string &t){ regi_str(t); vector>ret(s.size(),vector(s[0].size())); for(int i=0;i>to_int(const vector&s){ string t; for(int i=0;i&s,const string &t){ regi_int(t); string ret; for(auto z:s)ret+=dict[z]; return ret; } vector to_str(const vector>&s,const string &t){ regi_int(t); vectorret(s.size()); for(int i=0;i struct edge { int to; T cost; int id; edge():to(-1),id(-1){}; edge(int to, T cost = 1, int id = -1):to(to), cost(cost), id(id){} operator int() const { return to; } }; template using Graph = vector>>; template Graphrevgraph(const Graph &g){ Graphret(g.size()); for(int i=0;i Graph readGraph(int n,int m,int indexed=1,bool directed=false,bool weighted=false){ Graph ret(n); for(int es = 0; es < m; es++){ int u,v; T w=1; cin>>u>>v;u-=indexed,v-=indexed; if(weighted)cin>>w; ret[u].emplace_back(v,w,es); if(!directed)ret[v].emplace_back(u,w,es); } return ret; } template Graph readParent(int n,int indexed=1,bool directed=true){ Graphret(n); for(int i=1;i>p; p-=indexed; ret[p].emplace_back(i); if(!directed)ret[i].emplace_back(p); } return ret; } template< int mod > struct ModInt { int x; ModInt() : x(0) {} ModInt(int64_t y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {} ModInt &operator+=(const ModInt &p) { if((x += p.x) >= mod) x -= mod; return *this; } ModInt &operator-=(const ModInt &p) { if((x += mod - p.x) >= mod) 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 { return ModInt(-x); } 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; } bool operator==(const ModInt &p) const { return x == p.x; } bool operator!=(const ModInt &p) const { return x != p.x; } ModInt inverse() const { int a = x, b = mod, u = 1, v = 0, t; while(b > 0) { t = a / b; swap(a -= t * b, b); swap(u -= t * v, v); } return ModInt(u); } ModInt pow(int64_t n) const { ModInt ret(1), mul(x); while(n > 0) { if(n & 1) ret *= mul; mul *= mul; n >>= 1; } return ret; } pairfrac(){ for(int j=1;j<=300;j++){ for(int i=-300;i<=300;i++){ if(ModInt(i)/j==*this){ return make_pair(i,j); } } } return make_pair(-1,-1); } friend ostream &operator<<(ostream &os, const ModInt &p) { return os << p.x; } friend istream &operator>>(istream &is, ModInt &a) { int64_t t; is >> t; a = ModInt< mod >(t); return (is); } static int get_mod() { return mod; } }; template< typename T > struct Combination { vector< T > _fact, _rfact, _inv; Combination(ll sz) : _fact(sz + 1), _rfact(sz + 1), _inv(sz + 1) { _fact[0] = _rfact[sz] = _inv[0] = 1; for(ll i = 1; i <= sz; i++) _fact[i] = _fact[i - 1] * i; _rfact[sz] /= _fact[sz]; for(ll i = sz - 1; i >= 0; i--) _rfact[i] = _rfact[i + 1] * (i + 1); for(ll i = 1; i <= sz; i++) _inv[i] = _rfact[i] * _fact[i - 1]; } inline T fact(ll k) const { return _fact[k]; } inline T rfact(ll k) const { return _rfact[k]; } inline T inv(ll k) const { return _inv[k]; } T P(ll n, ll r) const { if(r < 0 || n < r) return 0; return fact(n) * rfact(n - r); } T C(ll p, ll q) const { if(q < 0 || p < q) return 0; return fact(p) * rfact(q) * rfact(p - q); } T RC(ll p, ll q) const { if(q < 0 || p < q) return 0; return rfact(p) * fact(q) * fact(p - q); } T H(ll n, ll r) const { if(n < 0 || r < 0) return (0); return r == 0 ? 1 : C(n + r - 1, r); } //+1がm個、-1がn個で prefix sumが常にk以上 T catalan(ll m,ll n,ll k){ if(n>m-k)return 0; else return C(n+m,m)-C(n+m,n+k-1); } }; using modint = ModInt< MOD9 >;modint mpow(ll n, ll x){return modint(n).pow(x);}modint mpow(modint n, ll x){return n.pow(x);} //using modint=ld;modint mpow(ll n, ll x){return pow(n,x);}modint mpow(modint n, ll x){return pow(n,x);} using Comb=Combination; template< typename Mint > struct NumberTheoreticTransformFriendlyModInt { static vector< Mint > dw, idw; static int max_base; static Mint root; NumberTheoreticTransformFriendlyModInt() = default; static void init() { const unsigned mod = Mint::get_mod(); assert(mod >= 3 && mod % 2 == 1); auto tmp = mod - 1; max_base = 0; while(tmp % 2 == 0) tmp >>= 1, max_base++; root = 2; while(root.pow((mod - 1) >> 1) == 1) root += 1; assert(root.pow(mod - 1) == 1); dw.resize(max_base); idw.resize(max_base); for(int i = 0; i < max_base; i++) { dw[i] = -root.pow((mod - 1) >> (i + 2)); idw[i] = Mint(1) / dw[i]; } } static void ntt(vector< Mint > &a) { const int n = (int) a.size(); assert((n & (n - 1)) == 0); assert(__builtin_ctz(n) <= max_base); for(int m = n; m >>= 1;) { Mint w = 1; for(int s = 0, k = 0; s < n; s += 2 * m) { for(int i = s, j = s + m; i < s + m; ++i, ++j) { auto x = a[i], y = a[j] * w; a[i] = x + y, a[j] = x - y; } w *= dw[__builtin_ctz(++k)]; } } } static void intt(vector< Mint > &a, bool f = true) { const int n = (int) a.size(); assert((n & (n - 1)) == 0); assert(__builtin_ctz(n) <= max_base); for(int m = 1; m < n; m *= 2) { Mint w = 1; for(int s = 0, k = 0; s < n; s += 2 * m) { for(int i = s, j = s + m; i < s + m; ++i, ++j) { auto x = a[i], y = a[j]; a[i] = x + y, a[j] = (x - y) * w; } w *= idw[__builtin_ctz(++k)]; } } if(f) { Mint inv_sz = Mint(1) / n; for(int i = 0; i < n; i++) a[i] *= inv_sz; } } static vector< Mint > multiply(vector< Mint > a, vector< Mint > b) { int need = a.size() + b.size() - 1; int nbase = 1; while((1 << nbase) < need) nbase++; int sz = 1 << nbase; a.resize(sz, 0); b.resize(sz, 0); ntt(a); ntt(b); Mint inv_sz = Mint(1) / sz; for(int i = 0; i < sz; i++) a[i] *= b[i] * inv_sz; intt(a, false); a.resize(need); return a; } }; template< typename Mint > vector< Mint > NumberTheoreticTransformFriendlyModInt::dw = vector< Mint >(); template< typename Mint > vector< Mint > NumberTheoreticTransformFriendlyModInt< Mint >::idw = vector< Mint >(); template< typename Mint > int NumberTheoreticTransformFriendlyModInt< Mint >::max_base = 0; template< typename Mint > Mint NumberTheoreticTransformFriendlyModInt< Mint >::root = 2; //ret[i-j]=x[i]*y[j] template vectormultiply_minus(vectorx,vectory){ reverse(y.begin(),y.end()); auto tmp = Conv::multiply(x,y); vectorret(x.size()); for(int i = 0; i < x.size(); i++){ ret[i] = tmp[y.size() - 1 + i]; } return ret; } //NumberTheoreticTransformFriendlyModInt::init(); template< typename T > struct FormalPowerSeriesFriendlyNTT : vector< T > { using vector< T >::vector; using P = FormalPowerSeriesFriendlyNTT; using NTT = NumberTheoreticTransformFriendlyModInt< T >; P pre(int deg) const { return P(begin(*this), begin(*this) + min((int) this->size(), deg)); } P rev(int deg = -1) const { P ret(*this); if(deg != -1) ret.resize(deg, T(0)); reverse(begin(ret), end(ret)); return ret; } void ntt(){ NTT::ntt(*this); } void intt(){ NTT::intt(*this); } void shrink() { while(this->size() && this->back() == T(0)) this->pop_back(); } P operator+(const P &r) const { return P(*this) += r; } P operator+(const T &v) const { return P(*this) += v; } P operator-(const P &r) const { return P(*this) -= r; } P operator-(const T &v) const { return P(*this) -= v; } P operator*(const P &r) const { return P(*this) *= r; } P operator*(const T &v) const { return P(*this) *= v; } P operator/(const P &r) const { return P(*this) /= r; } P operator%(const P &r) const { return P(*this) %= r; } P &operator+=(const P &r) { if(r.size() > this->size()) this->resize(r.size()); for(int i = 0; i < (int) r.size(); i++) (*this)[i] += r[i]; return *this; } P &operator-=(const P &r) { if(r.size() > this->size()) this->resize(r.size()); for(int i = 0; i < (int) r.size(); i++) (*this)[i] -= r[i]; return *this; } // https://judge.yosupo.jp/problem/convolution_mod P &operator*=(const P &r) { if(this->empty() || r.empty()) { this->clear(); return *this; } auto ret = NTT::multiply(*this, r); return *this = {begin(ret), end(ret)}; } P &operator/=(const P &r) { if(this->size() < r.size()) { this->clear(); return *this; } int n = this->size() - r.size() + 1; return *this = (rev().pre(n) * r.rev().inv(n)).pre(n).rev(n); } P &operator%=(const P &r) { *this -= *this / r * r; shrink(); return *this; } // https://judge.yosupo.jp/problem/division_of_polynomials pair< P, P > div_mod(const P &r) { P q = *this / r; P x = *this - q * r; x.shrink(); return make_pair(q, x); } P operator-() const { P ret(this->size()); for(int i = 0; i < (int) this->size(); i++) ret[i] = -(*this)[i]; return ret; } P &operator+=(const T &r) { if(this->empty()) this->resize(1); (*this)[0] += r; return *this; } P &operator-=(const T &r) { if(this->empty()) this->resize(1); (*this)[0] -= r; return *this; } P &operator*=(const T &v) { for(int i = 0; i < (int) this->size(); i++) (*this)[i] *= v; return *this; } P dot(P r) const { P ret(min(this->size(), r.size())); for(int i = 0; i < (int) ret.size(); i++) ret[i] = (*this)[i] * r[i]; return ret; } P operator>>(int sz) const { if((int) this->size() <= sz) return {}; P ret(*this); ret.erase(ret.begin(), ret.begin() + sz); return ret; } P operator<<(int sz) const { P ret(*this); ret.insert(ret.begin(), sz, T(0)); return ret; } T operator()(T x) const { T r = 0, w = 1; for(auto &v : *this) { r += w * v; w *= x; } return r; } P diff() const { const int n = (int) this->size(); P ret(max(0, n - 1)); for(int i = 1; i < n; i++) ret[i - 1] = (*this)[i] * T(i); return ret; } P integral() const { const int n = (int) this->size(); P ret(n + 1); ret[0] = T(0); for(int i = 0; i < n; i++) ret[i + 1] = (*this)[i] / T(i + 1); return ret; } // https://judge.yosupo.jp/problem/inv_of_formal_power_series // F(0) must not be 0 P inv(int deg = -1) const { assert(((*this)[0]) != T(0)); const int n = (int) this->size(); if(deg == -1) deg = n; P res(deg); res[0] = {T(1) / (*this)[0]}; for(int d = 1; d < deg; d <<= 1) { P f(2 * d), g(2 * d); for(int j = 0; j < min(n, 2 * d); j++) f[j] = (*this)[j]; for(int j = 0; j < d; j++) g[j] = res[j]; NTT::ntt(f); NTT::ntt(g); f = f.dot(g); NTT::intt(f); for(int j = 0; j < d; j++) f[j] = 0; NTT::ntt(f); for(int j = 0; j < 2 * d; j++) f[j] *= g[j]; NTT::intt(f); for(int j = d; j < min(2 * d, deg); j++) res[j] = -f[j]; } return res; } // https://judge.yosupo.jp/problem/log_of_formal_power_series // F(0) must be 1 P log(int deg = -1) const { assert((*this)[0] == T(1)); const int n = (int) this->size(); if(deg == -1) deg = n; return (this->diff() * this->inv(deg)).pre(deg - 1).integral(); } // https://judge.yosupo.jp/problem/sqrt_of_formal_power_series P sqrt(int deg = -1, const function< T(T) > &get_sqrt = [](T) { return T(1); }) const { const int n = (int) this->size(); if(deg == -1) deg = n; if((*this)[0] == T(0)) { for(int i = 1; i < n; i++) { if((*this)[i] != T(0)) { if(i & 1) return {}; if(deg - i / 2 <= 0) break; auto ret = (*this >> i).sqrt(deg - i / 2, get_sqrt); if(ret.empty()) return {}; ret = ret << (i / 2); if((int) ret.size() < deg) ret.resize(deg, T(0)); return ret; } } return P(deg, 0); } auto sqr = T(get_sqrt((*this)[0])); if(sqr * sqr != (*this)[0]) return {}; P ret{sqr}; T inv2 = T(1) / T(2); for(int i = 1; i < deg; i <<= 1) { ret = (ret + pre(i << 1) * ret.inv(i << 1)) * inv2; } return ret.pre(deg); } P sqrt(const function< T(T) > &get_sqrt, int deg = -1) const { return sqrt(deg, get_sqrt); } // https://judge.yosupo.jp/problem/exp_of_formal_power_series // F(0) must be 0 P exp(int deg = -1) const { if(deg == -1) deg = this->size(); assert((*this)[0] == T(0)); P inv; inv.reserve(deg + 1); inv.push_back(T(0)); inv.push_back(T(1)); auto inplace_integral = [&](P &F) -> void { const int n = (int) F.size(); auto mod = T::get_mod(); while((int) inv.size() <= n) { int i = inv.size(); inv.push_back((-inv[mod % i]) * (mod / i)); } F.insert(begin(F), T(0)); for(int i = 1; i <= n; i++) F[i] *= inv[i]; }; auto inplace_diff = [](P &F) -> void { if(F.empty()) return; F.erase(begin(F)); T coeff = 1, one = 1; for(int i = 0; i < (int) F.size(); i++) { F[i] *= coeff; coeff += one; } }; P b{1, 1 < (int) this->size() ? (*this)[1] : 0}, c{1}, z1, z2{1, 1}; for(int m = 2; m < deg; m *= 2) { auto y = b; y.resize(2 * m); NTT::ntt(y); z1 = z2; P z(m); for(int i = 0; i < m; ++i) z[i] = y[i] * z1[i]; NTT::intt(z); fill(begin(z), begin(z) + m / 2, T(0)); NTT::ntt(z); for(int i = 0; i < m; ++i) z[i] *= -z1[i]; NTT::intt(z); c.insert(end(c), begin(z) + m / 2, end(z)); z2 = c; z2.resize(2 * m); NTT::ntt(z2); P x(begin(*this), begin(*this) + min< int >(this->size(), m)); inplace_diff(x); x.push_back(T(0)); NTT::ntt(x); for(int i = 0; i < m; ++i) x[i] *= y[i]; NTT::intt(x); x -= b.diff(); x.resize(2 * m); for(int i = 0; i < m - 1; ++i) x[m + i] = x[i], x[i] = T(0); NTT::ntt(x); for(int i = 0; i < 2 * m; ++i) x[i] *= z2[i]; NTT::intt(x); x.pop_back(); inplace_integral(x); for(int i = m; i < min< int >(this->size(), 2 * m); ++i) x[i] += (*this)[i]; fill(begin(x), begin(x) + m, T(0)); NTT::ntt(x); for(int i = 0; i < 2 * m; ++i) x[i] *= y[i]; NTT::intt(x); b.insert(end(b), begin(x) + m, end(x)); } return P{begin(b), begin(b) + deg}; } // https://judge.yosupo.jp/problem/pow_of_formal_power_series P pow(int64_t k, int deg = -1) const { const int n = (int) this->size(); if(deg == -1) deg = n; for(int i = 0; i < n; i++) { if((*this)[i] != T(0)) { T rev = T(1) / (*this)[i]; P ret = (((*this * rev) >> i).log(deg) * k).exp() * ((*this)[i].pow(k)); if(i * k > deg) return P(deg, T(0)); ret = (ret << (i * k)).pre(deg); if((int) ret.size() < deg) ret.resize(deg, T(0)); return ret; } } return *this; } P mod_pow(int64_t k, P g) const { P modinv = g.rev().inv(); auto get_div = [&](P base) { if(base.size() < g.size()) { base.clear(); return base; } int n = base.size() - g.size() + 1; return (base.rev().pre(n) * modinv.pre(n)).pre(n).rev(n); }; P x(*this), ret{1}; while(k > 0) { if(k & 1) { ret *= x; ret -= get_div(ret) * g; ret.shrink(); } x *= x; x -= get_div(x) * g; x.shrink(); k >>= 1; } return ret; } // https://judge.yosupo.jp/problem/polynomial_taylor_shift P taylor_shift(T c) const { int n = (int) this->size(); vector< T > fact(n), rfact(n); fact[0] = rfact[0] = T(1); for(int i = 1; i < n; i++) fact[i] = fact[i - 1] * T(i); rfact[n - 1] = T(1) / fact[n - 1]; for(int i = n - 1; i > 1; i--) rfact[i - 1] = rfact[i] * T(i); P p(*this); for(int i = 0; i < n; i++) p[i] *= fact[i]; p = p.rev(); P bs(n, T(1)); for(int i = 1; i < n; i++) bs[i] = bs[i - 1] * c * rfact[i] * fact[i - 1]; p = (p * bs).pre(n); p = p.rev(); for(int i = 0; i < n; i++) p[i] *= rfact[i]; return p; } void mul(vector> g, bool extend = false){ if(extend)this->resize(this->size() + g.back().first); int n = this->size(); int d = g[0].first; T c = g[0].second; if(d == 0)g.erase(g.begin()); else c = 0; for(int i = n - 1; i >= 0; i--){ (*this)[i] *= c; for(auto z : g){ if(z.first > i)continue; (*this)[i] += (*this)[i-z.first] * z.second; } } } void div(vector>g){//定数項は非ゼロ int n = this->size(); int d = g[0].first; T c = g[0].second; c = T(1) / c; g.erase(g.begin()); for(int i = 0; i < n; i++){ for(auto z : g){ if(z.first > i)continue; (*this)[i] -= (*this)[i-z.first] * z.second; } (*this)[i] *= c; } } template P recover(const C &comb){ int sz = this->size(); P x(sz),y(sz); for(int i = 0; i < sz; i++){ x[sz - i - 1] = (*this)[i] * comb.fact(i); y[i] = comb.rfact(i) * (i % 2 == 0 ? 1 : -1); } P tmp(sz); rep(i,0,sz)tmp[i]=comb.rfact(i); auto z = x * y; P ret(z.begin(), z.begin() + sz); reverse(ret.begin(), ret.end()); for(int i = 0; i < sz; i++){ ret[i] *= comb.rfact(i); } return ret; } }; template< typename Mint > using FPS = FormalPowerSeriesFriendlyNTT< Mint >; template Poly multiply_all(vector&fs){ queueque; for(auto f:fs)que.push(f); while(que.size()>=2){ auto p=que.front(); que.pop(); auto q=que.front(); que.pop(); que.push(p*q); } return que.front(); } // sum f[i]/g[i] template Poly sum_of_fractions(vector&f,vector&g,int deg){ queue>que; assert(f.size()==g.size()); for(int i=0;i=2){ auto p=que.front(); que.pop(); auto q=que.front(); que.pop(); que.emplace(p.first*q.second+p.second*q.first,p.second*q.second); } return que.front().first*(que.front().second.inv(deg)); } template using FormalPowerSeries=FormalPowerSeriesFriendlyNTT; using fps=FormalPowerSeriesFriendlyNTT; //mainに持っていくこと! int main(){ cin.tie(nullptr); ios_base::sync_with_stdio(false); ll res=0,buf=0; bool judge = true; ll k;cin>>k; Comb comb(50000); ll n=30000; vectorret(n+1); // rep(i,1,n+1){ // rep(j,1,i+1){ // rep(o,1,j+1){ // if(i+j+o>n)continue; // modint add=comb.fact(i+j+o)/comb.fact(o)/comb.fact(j+1)*(j-o+1)/comb.fact(i+2)*(i-j+1)*(i-o+2); // //OUT(i,j,o,add); // ret[i+j+o]+=mpow(i,k)*add*add; // } // } // } // OUT(ret); // return 0; //(j-o+1)*(i-j+1)*(i-o+2) NumberTheoreticTransformFriendlyModInt::init(); vectorpower(3*n+3); rep(i,0,n+1)power[i]=mpow(i,k); rep(b,0,64){ //1:j or 1-o //2:i or 1-j //4:i or 2-o auto g2=[&](ll i){ modint ret=comb.rfact(i+2)*comb.rfact(i+2)*power[i]; if(~b&2)ret*=i; if(~b&16)ret*=i; if(~b&4)ret*=i; if(~b&32)ret*=i; return ret; }; auto g1=[&](ll j){ modint ret=comb.rfact(j+1)*comb.rfact(j+1); if(~b&1)ret*=j; if(~b&8)ret*=j; if(b&2)ret*=1-j; if(b&16)ret*=1-j; return ret; }; auto g0=[&](ll o){ modint ret=comb.rfact(o)*comb.rfact(o); if(b&1)ret*=1-o; if(b&8)ret*=1-o; if(b&4)ret*=2-o; if(b&32)ret*=2-o; return ret; }; // rep(i,1,n+1)rep(j,1,i+1)rep(o,1,j+1){ // if(i+j+o<=n)ret[i+j+o]+=g2(i)*g1(j)*g0(o); // } auto rec=[&](auto &&rec,int l,int r)->pair { pairfp(fps(2*(r-l)+1),fps(2*(r-l)+1)); if(r-l==1){ if(3*l<=n){ //OUT(l,r,ret[3*l]); ret[3*l]+=g0(l)*g1(l)*g2(l); //OUT(l,r,ret[3*l]); } if(2*l<=n){ fp.fi[0]+=g0(l)*g1(l); fp.se[0]+=g1(l)*g2(l); } return fp; } ll m=(l+r)/2; auto [lf01,lf12]=rec(rec,l,m); auto [rf01,rf12]=rec(rec,m,r); fps rf2(r-m); { rep(o,m,r)rf2[o-m]=g2(o); auto g=lf01*rf2; rep(i,0,g.size()){ if(i+2*l+m<=n){ ret[i+2*l+m]+=g[i]; } } } fps lf0(m-l); { rep(i,l,m)lf0[i-l]=g0(i); auto g=lf0*rf12; rep(i,0,g.size()){ if(i+l+2*m<=n){ ret[i+l+2*m]+=g[i]; } } } rep(i,0,lf01.size())fp.fi[i]+=lf01[i]; rep(i,0,rf01.size())fp.fi[i+2*(m-l)]+=rf01[i]; rep(i,0,lf12.size())fp.se[i]+=lf12[i]; rep(i,0,rf12.size())fp.se[i+2*(m-l)]+=rf12[i]; fps lf1(m-l); rep(i,l,m)lf1[i-l]=g1(i); fps rf1(r-m); rep(i,m,r)rf1[i-m]=g1(i); { auto g=lf0*rf1; rep(i,0,g.size()){ fp.fi[i+(m-l)]+=g[i]; } } { auto g=lf1*rf2; rep(i,0,g.size()){ fp.se[i+(m-l)]+=g[i]; } } return fp; }; rec(rec,1,n+1); }; rep(i,1,n+1){ ret[i]*=comb.fact(i)*comb.fact(i); } cout<