# Submit Info #57665

Problem Lang User Status Time Memory
Polynomial Taylor Shift cpp snuke AC 262 ms 24.07 MiB

ケース詳細
Name Status Time Memory
example_00 AC 1 ms 0.37 MiB
example_01 AC 1 ms 0.61 MiB
fft_killer_00 AC 261 ms 24.07 MiB
fft_killer_01 AC 262 ms 24.06 MiB
max_random_00 AC 260 ms 24.07 MiB
max_random_01 AC 260 ms 24.06 MiB
medium_00 AC 1 ms 0.73 MiB
medium_01 AC 3 ms 0.96 MiB
medium_02 AC 3 ms 0.96 MiB
medium_all_zero_00 AC 1 ms 0.70 MiB
medium_c_zero_00 AC 1 ms 0.72 MiB
random_00 AC 214 ms 22.22 MiB
random_01 AC 239 ms 22.67 MiB
random_02 AC 28 ms 3.16 MiB
small_00 AC 1 ms 0.61 MiB
small_01 AC 1 ms 0.60 MiB
small_02 AC 1 ms 0.62 MiB
small_03 AC 1 ms 0.61 MiB
small_04 AC 1 ms 0.61 MiB
small_05 AC 1 ms 0.61 MiB
small_06 AC 1 ms 0.61 MiB
small_07 AC 1 ms 0.62 MiB
small_08 AC 1 ms 0.36 MiB
small_09 AC 1 ms 0.61 MiB
small_10 AC 1 ms 0.62 MiB
small_11 AC 1 ms 0.61 MiB
small_12 AC 1 ms 0.61 MiB
small_13 AC 1 ms 0.62 MiB
small_14 AC 1 ms 0.61 MiB
small_15 AC 1 ms 0.61 MiB

#include <bits/stdc++.h> #define fi first #define se second #define rep(i,n) for(int i = 0; i < (n); ++i) #define rrep(i,n) for(int i = 1; i <= (n); ++i) #define drep(i,n) for(int i = (n)-1; i >= 0; --i) #define srep(i,s,t) for (int i = s; i < (t); ++i) #define dsrep(i,t,s) for(int i = (t)-1; i >= (s); --i) #define rng(a) a.begin(),a.end() #define rrng(a) a.rbegin(),a.rend() #define isin(x,l,r) ((l) <= (x) && (x) < (r)) #define pb push_back #define eb emplace_back #define sz(x) (int)(x).size() #define pcnt __builtin_popcountll #define snuke srand((unsigned)clock()+(unsigned)time(NULL)); #define show(x) cerr<<#x<<" = "<<x<<endl; #define bn(x) ((1<<(x))-1) #define newline puts("") using namespace std; template<typename T> using vc = vector<T>; template<typename T> using vv = vc<vc<T>>; template<typename T> using PQ = priority_queue<T,vc<T>,greater<T> >; using ll = long long; using uint = unsigned; using ull = unsigned long long; using P = pair<int,int>; using T3 = tuple<int,int,int>; using vi = vc<int>; using vvi = vv<int>; using vl = vc<ll>; using vp = vc<P>; using vt = vc<T3>; int getInt(){int x;scanf("%d",&x);return x;} vi pm(int n, int s=0) { vi a(n); iota(rng(a),s); return a;} template<typename T>istream& operator>>(istream&i,vc<T>&v){rep(j,sz(v))i>>v[j];return i;} template<typename T>string join(const T&v,const string& d=""){stringstream s;rep(i,sz(v))(i?s<<d:s)<<v[i];return s.str();} template<typename T>ostream& operator<<(ostream&o,const vc<T>&v){if(sz(v))o<<join(v," ");return o;} template<typename T1,typename T2>istream& operator>>(istream&i,pair<T1,T2>&v){return i>>v.fi>>v.se;} template<typename T1,typename T2>ostream& operator<<(ostream&o,const pair<T1,T2>&v){return o<<v.fi<<","<<v.se;} vc<string> split(const string& s,char d=' '){vc<string> r(1);for(char c:s)if(c==d)r.pb("");else r.back()+=c;return r;} string operator*(const string& s,int t){return join(vc<string>(t,s));} template<typename T1,typename T2>bool mins(T1& x,const T2&y){if(x>y){x=y;return true;}else return false;} template<typename T1,typename T2>bool maxs(T1& x,const T2&y){if(x<y){x=y;return true;}else return false;} template<typename Tx, typename Ty>Tx dup(Tx x, Ty y){return (x+y-1)/y;} template<typename T>ll suma(const vc<T>&a){ll res(0);for(auto&&x:a)res+=x;return res;} template<typename T>void uni(T& a){sort(rng(a));a.erase(unique(rng(a)),a.end());} const double eps = 1e-10; const ll LINF = 1001002003004005006ll; const int INF = 1001001001; #define dame { puts("-1"); return;} #define yn {puts("Yes");}else{puts("No");} const int MX = 200005; // Mod int const uint mod = 998244353; struct mint { uint x; mint(): x(0) {} mint(ll x):x((x%mod+mod)%mod) {} mint operator-() const { return mint(0) - *this;} mint operator~() const { return mint(1) / *this;} mint& operator+=(const mint& a) { if((x+=a.x)>=mod) x-=mod; return *this;} mint& operator-=(const mint& a) { if((x+=mod-a.x)>=mod) x-=mod; return *this;} mint& operator*=(const mint& a) { x=(ull)x*a.x%mod; return *this;} mint& operator/=(const mint& a) { x=(ull)x*a.pow(mod-2).x%mod; return *this;} mint operator+(const mint& a) const { return mint(*this) += a;} mint operator-(const mint& a) const { return mint(*this) -= a;} mint operator*(const mint& a) const { return mint(*this) *= a;} mint operator/(const mint& a) const { return mint(*this) /= a;} mint pow(ll t) const { if(!t) return 1; mint res = pow(t/2); res *= res; return (t&1)?res*x:res; } bool operator<(const mint& a) const { return x < a.x;} bool operator==(const mint& a) const { return x == a.x;} bool operator!=(const mint& a) const { return x != a.x;} }; mint ex(mint x, ll t) { return x.pow(t);} istream& operator>>(istream&i,mint&a) {i>>a.x;return i;} //* ostream& operator<<(ostream&o,const mint&a) {o<<a.x;return o;} /*/ ostream& operator<<(ostream&o, const mint&x) { int a = x.x, b = 1; rep(s,2)rrep(i,1000) { int y = ((s?-x:x)*i).x; if (abs(a)+b > y+i) a = s?-y:y, b = i; } o<<a; if (b != 1) o<<'/'<<b; return o; }//*/ using vm = vector<mint>; using vvm = vector<vm>; struct comb { vm f, g; comb() {} comb(int mx): f(mx+1), g(mx+1) { f[0] = 1; rrep(i,mx) f[i] = f[i-1]*i; g[mx] = f[mx].pow(mod-2); for(int i = mx; i > 0; --i) g[i-1] = g[i]*i; } mint operator()(int a, int b) { if (a < b || b < 0) return 0; return f[a]*g[b]*g[a-b]; } }; // struct NTT { int ceil_pow2(int n) { int x = 0; while ((1U<<x) < (uint)(n)) x++; return x;} int bsf(uint n) { return __builtin_ctz(n);} const static int _g = 3; // primitive root !!! void butterfly(vm& a) { static mint g = _g; int n = sz(a), h = ceil_pow2(n); static bool first = true; static mint sum_e[30]; if (first) { first = false; mint es[30], ies[30]; int cnt2 = bsf(mod - 1); mint e = g.pow((mod - 1) >> cnt2), ie = ~e; for (int i = cnt2; i >= 2; i--) { es[i - 2] = e; ies[i - 2] = ie; e *= e; ie *= ie; } mint now = 1; rep(i,cnt2-1) sum_e[i] = es[i] * now, now *= ies[i]; } rrep(ph,h) { int w = 1<<(ph-1), p = 1<<(h-ph); mint now = 1; rep(s,w) { int offset = s << (h - ph + 1); for (int i = 0; i < p; i++) { auto l = a[i + offset], r = a[i + offset + p] * now; a[i + offset] = l + r; a[i + offset + p] = l - r; } now *= sum_e[bsf(~(uint)(s))]; } } } void butterfly_inv(vm& a) { static mint g = _g; int n = sz(a), h = ceil_pow2(n); static bool first = true; static mint sum_ie[30]; if (first) { first = false; mint es[30], ies[30]; int cnt2 = bsf(mod - 1); mint e = g.pow((mod - 1) >> cnt2), ie = ~e; for (int i = cnt2; i >= 2; i--) { es[i - 2] = e; ies[i - 2] = ie; e *= e; ie *= ie; } mint now = 1; rep(i,cnt2-1) sum_ie[i] = ies[i] * now, now *= es[i]; } for (int ph = h; ph >= 1; ph--) { int w = 1 << (ph - 1), p = 1 << (h - ph); mint inow = 1; rep(s,w) { int offset = s << (h - ph + 1); for (int i = 0; i < p; i++) { auto l = a[i + offset], r = a[i + offset + p]; a[i + offset] = l + r; a[i + offset + p] = (ull)(mod + l.x - r.x) * inow.x; } inow *= sum_ie[bsf(~(uint)(s))]; } } } vm operator()(vm a, vm b) { int n = sz(a), m = sz(b); if (!n || !m) return {}; if (min(n, m) <= 60) { if (n < m) swap(n, m), swap(a, b); vm ans(n+m-1); rep(i,n)rep(j,m) ans[i + j] += a[i] * b[j]; return ans; } int z = 1 << ceil_pow2(n+m-1); a.resize(z); butterfly(a); b.resize(z); butterfly(b); rep(i,z) a[i] *= b[i]; butterfly_inv(a); a.resize(n + m - 1); mint iz = ~(mint(z)); rep(i,n+m-1) a[i] *= iz; return a; } } ntt; struct modinv { int n; vm d; modinv(): n(2), d({0,1}) {} mint operator()(int i) { while (n <= i) d.pb(-d[mod%n]*(mod/n)), ++n; return d[i];} mint operator[](int i) const { return d[i];} } invs; struct modfact { int n; vm d; modfact(): n(2), d({1,1}) {} mint operator()(int i) { while (n <= i) d.pb(d.back()*n), ++n; return d[i];} mint operator[](int i) const { return d[i];} } facts; struct modfactinv { int n; vm d; modfactinv(): n(2), d({1,1}) {} mint operator()(int i) { while (n <= i) d.pb(d.back()*invs(n)), ++n; return d[i];} mint operator[](int i) const { return d[i];} } ifacts; struct fps : vm { #define d (*this) #define s int(vm::size()) template<class...Args> fps(Args...args): vm(args...) {} fps(initializer_list<mint> a): vm(rng(a)) {} int size() const { return vm::size();} void rsz(int n) { if (s < n) resize(n);} fps& low_(int n) { resize(n); return d;} fps low(int n) const { return fps(d).low_(n);} fps low(fps a, int n) const { return a.low_(n);} fps& rev_() { reverse(rng(d)); return d;} fps rev() const { return fps(d).rev_();} fps rev(fps a) const { return a.rev_();} mint& operator[](int i) { rsz(i+1); return vm::operator[](i);} mint operator[](int i) const { return i<s ? vm::operator[](i) : 0;} mint operator()(mint x) const { mint r; drep(i,s) r = r*x+d[i]; return r;} fps operator<<(int a) const { fps r(d); r.insert(r.begin(), a, 0); return r;} fps operator>>(int a) const { fps r(d); r.rsz(a); r.erase(r.begin(), r.begin()+a); return r;} fps& fit() { while (s && !back().x) pop_back(); return d;} fps operator-() const { fps r(d); rep(i,s) r[i] = -r[i]; return r;} fps& operator+=(const fps& a) { rsz(sz(a)); rep(i,sz(a)) d[i] += a[i]; return d;} fps& operator-=(const fps& a) { rsz(sz(a)); rep(i,sz(a)) d[i] -= a[i]; return d;} fps& operator*=(const fps& a) { return d = ntt(d, a);} fps& operator/=(const fps& a) { int w = s-sz(a)+1; if (w <= 0) return d = 0; return (rev_().low_(w) *= a.rev().inv(w)).low_(w).rev_(); } fps& operator%=(const fps& a) { return (d -= d/a*a).low_(sz(a)-1);} fps& operator*=(mint a) { rep(i,s) d[i] *= a; return d;} fps& operator/=(mint a) { return d *= ~a;} fps& operator*=(int a) { return d *= mint(a);} fps& operator/=(int a) { return d /= mint(a);} fps operator+(const fps& a) const { return fps(d) += a;} fps operator-(const fps& a) const { return fps(d) -= a;} fps operator*(const fps& a) const { return fps(d) *= a;} fps operator/(const fps& a) const { return fps(d) /= a;} fps operator%(const fps& a) const { return fps(d) %= a;} fps operator*(mint a) const { return fps(d) *= a;} fps operator/(mint a) const { return fps(d) *= ~a;} fps operator*(int a) const { return fps(d) *= mint(a);} fps operator/(int a) const { return fps(d) /= mint(a);} fps& mul1(mint a) { pb(0); drep(i,s-1) d[i+1] += d[i], d[i] *= a; return d;} // *=(x+a), /=(x+a) fps& div1(mint a) { mint pre = back(); pop_back(); drep(i,s) std::swap(pre, d[i]), pre -= d[i]*a; return d;} fps dif() const { fps r(s-1); rrep(i,sz(r)) r[i-1] = d[i]*i; return r;} fps integ() const { fps r(s+1); rrep(i,s) r[i] = d[i-1]*invs(i); return r;} fps inv() const { return inv(s);} fps inv(int w) const { fps r({~d[0]}); for (int i = 1; i < w; i <<= 1) r = r*2 - low(r*r*low(i<<1), i<<1); return r.low_(w); } vm operator()(const vm& x) const { int n = sz(x), n2 = n<<1; vc<fps> t(n2); rep(i,n) t[n+i] = {-x[i],1}; for (int i = n-1; i; --i) t[i] = t[i<<1]*t[i<<1|1]; t[1] = d%t[1]; srep(i,2,n2) t[i] = t[i>>1]%t[i]; vm r(n); rep(i,n) r[i] = t[n+i][0]; return r; } fps taylorShift(mint c) const { fps res; vm a(s), b(s,1); rep(i,s) a[i] = d[i]*facts(i); drep(i,s-1) b[i] = b[i+1]*c; rep(i,s) b[i] *= ifacts(s-1-i); a = ntt(a,b); rep(i,s) res[i] = a[s-1+i]*ifacts[i]; return res; } #undef s #undef d }; struct Solver { void solve() { int n,c; scanf("%d%d",&n,&c); fps a(n); cin>>a; a = a.taylorShift(c); cout<<a<<endl; } }; int main() { int ts = 1; // scanf("%d",&ts); rrep(ti,ts) { Solver solver; solver.solve(); } return 0; }