結果
| 問題 | No.3619 Compositional Power with Schröder Coordinate |
| コンテスト | |
| ユーザー |
 noya2
|
| 提出日時 | 2026-08-09 05:37:53 |
| 言語 | C++23 (gcc 15.2.0 + boost 1.90.0) |
| 結果 |
WA
|
| 実行時間 | - |
| コード長 | 28,059 bytes |
| 記録 | |
| コンパイル時間 | 3,117 ms |
| コンパイル使用メモリ | 365,484 KB |
| 実行使用メモリ | 90,440 KB |
| 最終ジャッジ日時 | 2026-08-10 20:52:58 |
| 合計ジャッジ時間 | 8,640 ms |
|
ジャッジサーバーID （参考情報） |
judge3_0 / judge1_0 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | WA * 2 |
| other | AC * 1 WA * 5 |
ソースコード
#line 1 "sol/ac_noya2.cpp"
#include<bits/stdc++.h>
using namespace std;
#line 2 "etc/fps_nachia.hpp"
using namespace std;
// https://judge.yosupo.jp/submission/133527
// https://judge.yosupo.jp/submission/199636
// https://judge.yosupo.jp/submission/199637
namespace nachia{
// ax + by = gcd(a,b)
// return ( x, - )
std::pair<long long, long long> ExtGcd(long long a, long long b){
long long x = 1, y = 0;
while(b){
long long u = a / b;
std::swap(a-=b*u, b);
std::swap(x-=y*u, y);
}
return std::make_pair(x, a);
}
} // namespace nachia
namespace nachia{
template<unsigned int MOD>
struct PrimitiveRoot{
using u64 = unsigned long long;
static constexpr u64 powm(u64 a, u64 i) {
u64 res = 1, aa = a;
for( ; i; i /= 2){
if(i & 1) res = res * aa % MOD;
aa = aa * aa % MOD;
}
return res;
}
static constexpr bool ExamineVal(unsigned int g){
u64 t = MOD - 1;
for(u64 d=2; d*d<=t; d+=1+(d&1)) if(t % d == 0){
if(powm(g, (MOD - 1) / d) == 1) return false;
while(t % d == 0) t /= d;
}
if(t != 1) if(powm(g, (MOD - 1) / t) == 1) return false;
return true;
}
static constexpr unsigned int GetVal(){
for(u64 x=2; x<MOD; x++) if(ExamineVal(x)) return x;
return 0;
}
static const unsigned int val = GetVal();
};
} // namespace nachia
namespace nachia{
int Popcount(unsigned long long c) noexcept {
#ifdef __GNUC__
return __builtin_popcountll(c);
#else
c = (c & (~0ull/3)) + ((c >> 1) & (~0ull/3));
c = (c & (~0ull/5)) + ((c >> 2) & (~0ull/5));
c = (c & (~0ull/17)) + ((c >> 4) & (~0ull/17));
c = (c * (~0ull/257)) >> 56;
return c;
#endif
}
// please ensure x != 0
int MsbIndex(unsigned long long x) noexcept {
#ifdef __GNUC__
return 63 - __builtin_clzll(x);
#else
using u64 = unsigned long long;
int q = (x >> 32) ? 32 : 0;
auto m = x >> q;
constexpr u64 hi = 0x8888'8888;
constexpr u64 mi = 0x1111'1111;
m = (((m | ~(hi - (m & ~hi))) & hi) * mi) >> 35;
m = (((m | ~(hi - (x & ~hi))) & hi) * mi) >> 31;
q += (m & 0xf) << 2;
q += 0x3333'3333'2222'1100 >> (((x >> q) & 0xf) << 2) & 0xf;
return q;
#endif
}
// please ensure x != 0
int LsbIndex(unsigned long long x) noexcept {
#ifdef __GNUC__
return __builtin_ctzll(x);
#else
return MsbIndex(x & -x);
#endif
}
}
namespace nachia {
template<class mint>
struct NttInterface{
template<class Iter>
void Butterfly(Iter, int) const {}
template<class Iter>
void IButterfly(Iter, int) const {}
template<class Iter>
void BitReversal(Iter a, int N) const {
for(int i=0, j=0; j<N; j++){
if(i < j) std::swap(a[i], a[j]);
for(int k = N>>1; k > (i^=k); k>>=1);
}
}
};
} // namespace nachia
#line 123 "etc/fps_nachia.hpp"
namespace nachia{
template <class mint>
struct Ntt : NttInterface<mint> {
using u32 = unsigned int;
using u64 = unsigned long long;
static int ceil_pow2(int n) {
int x = 0;
while ((1U << x) < (u32)(n)) x++;
return x;
}
static constexpr int bsf_constexpr(unsigned int n) {
int x = 0;
while (!(n & (1 << x))) x++;
return x;
}
struct fft_info {
static constexpr u32 g = nachia::PrimitiveRoot<mint::mod()>::val;
static constexpr int rank2 = bsf_constexpr(mint::mod()-1);
using RootTable = std::array<mint, rank2+1>;
RootTable root, iroot, rate3, irate3;
fft_info(){
root[rank2] = mint(g).pow((mint::mod() - 1) >> rank2);
iroot[rank2] = root[rank2].inv();
for(int i=rank2-1; i>=0; i--){
root[i] = root[i+1] * root[i+1];
iroot[i] = iroot[i+1] * iroot[i+1];
}
mint prod = 1, iprod = 1;
for(int i=0; i<=rank2-3; i++){
rate3[i] = root[i+3] * prod;
irate3[i] = iroot[i+3] * iprod;
prod *= iroot[i+3];
iprod *= root[i+3];
}
}
};
template<class RandomAccessIterator>
void ButterflyLayered(RandomAccessIterator a, int n, int stride, int repeat) const {
static const fft_info info;
int h = n * stride;
while(repeat--){
int len = 1;
int p = h;
if(ceil_pow2(n)%2 == 1){
p >>= 1;
for(int i=0; i<p; i++){
mint l = a[i], r = a[i+p];
a[i] = l+r; a[i+p] = l-r;
}
len <<= 1;
}
for( ; p > stride; ){
p >>= 2;
mint rot = 1, imag = info.root[2];
u64 mod2 = u64(mint::mod()) * mint::mod();
int offset = p;
for(int s=0; s<len; s++){
if(s) rot *= info.rate3[LsbIndex(~(u32)(s-1))];
mint rot2 = rot * rot;
mint rot3 = rot2 * rot;
for(int i=offset-p; i<offset; i++){
u64 a0 = u64(a[i].val());
u64 a1 = u64(a[i+p].val()) * rot.val();
u64 a2 = u64(a[i+2*p].val()) * rot2.val();
u64 a3 = u64(a[i+3*p].val()) * rot3.val();
u64 a1na3imag = u64(mint(a1 + mod2 - a3).val()) * imag.val();
u64 na2 = mod2 - a2;
a[i] = a0 + a2 + a1 + a3;
a[i+1*p] = a0 + a2 + (2 * mod2 - (a1 + a3));
a[i+2*p] = a0 + na2 + a1na3imag;
a[i+3*p] = a0 + na2 + (mod2 - a1na3imag);
}
offset += p << 2;
}
len <<= 2;
}
a += h;
}
}
template<class RandomAccessIterator>
void Butterfly(RandomAccessIterator a, int n) const {
ButterflyLayered(a, n, 1, 1);
}
template<class RandomAccessIterator>
void IButterflyLayered(RandomAccessIterator a, int n, int stride, int repeat) const {
static const fft_info info;
constexpr int MOD = mint::mod();
while(repeat--){
int len = n;
int p = stride;
for( ; 2 < len; ){
len >>= 2;
mint irot = 1, iimag = info.iroot[2];
int offset = p;
for(int s=0; s<len; s++){
if(s) irot *= info.irate3[LsbIndex(~(u32)(s-1))];
mint irot2 = irot * irot;
mint irot3 = irot2 * irot;
for(int i=offset-p; i<offset; i++){
u64 a0 = a[i].val();
u64 a1 = a[i+p].val();
u64 a2 = a[i+2*p].val();
u64 a3 = a[i+3*p].val();
u64 a2na3iimag = mint((a2 + MOD - a3) * iimag.val()).val();
a[i] = a0 + a1 + a2 + a3;
a[i+p] = (a0 + (MOD - a1) + a2na3iimag) * irot.val();
a[i+2*p] = (a0 + a1 + (MOD - a2) + (MOD - a3)) * irot2.val();
a[i+3*p] = (a0 + (MOD - a1) + (MOD - a2na3iimag)) * irot3.val();
}
offset += p << 2;
}
p <<= 2;
}
if(len == 2){
for(int i=0; i<p; i++){
mint l = a[i], r = a[i+p];
a[i] = l+r; a[i+p] = l-r;
}
p <<= 1;
}
a += p;
}
}
template<class RandomAccessIterator>
void IButterfly(RandomAccessIterator a, int n) const {
IButterflyLayered(a, n, 1, 1);
}
};
} // namespace nachia
namespace nachia{
template<class Fps>
Fps PolynomialTaylorShift(Fps f, typename Fps::ElemTy c){
int n = f.size();
Fps C = Fps(n).set(0,1);
for(int i=1; i<n; i++) C[i] = C[i-1] * c;
return f.timesFactorial().convolve(
C.timesInvFactorial().reverse()).clip(n-1,2*n-1).timesInvFactorial().move();
}
template<class Fps>
Fps FpsAntiTaylorShift(Fps f, typename Fps::ElemTy c){
int n = f.size();
Fps C = Fps(n).set(0,1);
for(int i=1; i<n; i++) C[i] = C[i-1] * c;
return f.timesInvFactorial().convolve(
C.timesInvFactorial(),n).timesFactorial().move();
}
} // namespace nachia
namespace nachia{
template<class Fps>
Fps CompositionOfFps(int N, Fps f, Fps g){
using Elem = typename Fps::ElemTy;
auto Zero = Elem(0);
auto One = Elem(1);
if(g.getCoeff(0).val() != 0){
f = PolynomialTaylorShift<Fps>(f, g[0]);
g[0] = Zero;
}
int n = 1; while(n < N) n *= 2;
n *= 2;
auto q = g.clip(0, n/2, 0, n/2).negate();
q[0] += One;
Fps q2(n*2), q1(n);
int d = n/2;
int e = 1;
std::vector<Fps> G;
auto qbuf = Fps(n);
auto invn = Elem(n).inv();
static auto ntt = Ntt<Elem>();
auto bat = [&](Fps& a, int s, int z, int r){
ntt.ButterflyLayered(a.begin(), z, s, r);
};
auto ibat = [&](Fps& a, int s, int z, int r){
ntt.IButterflyLayered(a.begin(), z, s, r);
};
while(true){
int fg = (d <= e ? 1 : 0);
int m = n/2;
for(int t=0; t<2; t++){
if(fg^t){
ibat(q, d, e, 1);
if(d == 1) break;
for(int i=0; i<d; i++) q1[i] = q[i];
for(int i=0; i<m; i++) q1[d+i] = Zero;
for(int i=d; i<m; i++) q1[m+i] = q[i];
bat(q1, d, e*2, 1);
e *= 2; m *= 2;
} else {
for(int i=0; i<m*2; i+=d*2){
for(int j=0; j<d; j++) q1[i+j] = q[i/2+j];
for(int j=0; j<d; j++) q1[i+d+j] = Zero;
}
bat(q1, 1, d*2, e);
d *= 2; m *= 2;
}
std::swap(q, q1); std::swap(q1, q2);
}
if(d == 1) break;
for(int i=0; i<n; i++) q[n+i] -= One + One;
for(int i=0; i<n; i++) std::swap(q[i*2], q[i*2+1]);
G.push_back(q.clip(0,n*2).move());
for(int x=0; x<n*2; x+=d) for(int y=1; y<d; y*=2) G.back().revRange(x+y,x+y*2);
std::swap(q, q1); std::swap(q1, q2);
d /= 2;
for(int i=0; i<n; i++) q1[i] = q2[i*2] * q2[i*2+1];
ibat(q1, 1, d, e);
d /= 2;
for(int i=0; i<n; i+=d*2) for(int j=0; j<d; j++) q[i/2+j] = q1[i+j];
q.times(invn);
}
for(int i=0; i<n/2; i++) q[n/2-1-i] = f.getCoeff(i);
while(G.size()){
bat(q,d,e,1);
for(int i=0; i<n; i+=d*2){
q1[i] = Zero;
for(int j=0; j<d; j++) q1[i+j+1] = q[i/2+j];
for(int j=1; j<d; j++) q1[i+d+j] = Zero;
}
d *= 2;
bat(q1,1,d,e);
auto qnntt = G.back().move(); G.pop_back();
for(int i=0; i<n; i++){
q2[i*2] = q1[i] * qnntt[i*2];
q2[i*2+1] = q1[i] * qnntt[i*2+1];
}
q2.times(invn/2);
ibat(q2,1,d*2,e);
for(int i=0; i<n*2; i+=d*2) for(int j=0; j<d; j++) q1[i/2+j] = q2[i+j+1];
ibat(q1,d,e,1);
e /= 2;
for(int i=0; i<n/2; i++) q[i] = q1[i];
}
return q.clip(d-N,d).reverse().move();
}
} // namespace nachia
namespace nachia {
// ret(y) = [x^k] g(x) / ( 1 - y f(x) )
// [y^j] ret(y) = [x^k] g f^j
template<class Fps>
std::vector<typename Fps::ElemTy> FpsSampleCoefficientOfPowers(Fps f, Fps g, int maxPower, int coeffAt){
using Elem = typename Fps::ElemTy;
auto Zero = Elem(0);
auto One = Elem(1);
int n = 1;
while(n < std::max(coeffAt + 1, maxPower + 1)) n *= 2;
n *= 2;
auto p = g.clip(0, coeffAt+1, n/2-1-coeffAt, n/2);
auto q = f.clip(0, n/2, 0, n/2).negate();
q[0] += One;
Fps p2(n*2), p1(n), q2(n*2), q1(n);
int d = n/2;
int e = 1;
auto pcoeff = One;
auto invn = Elem(n).inv();
static auto ntt = Ntt<Elem>();
auto bat = [&](Fps& a, int s, int z, int r){
ntt.ButterflyLayered(a.begin(), z, s, r);
};
auto ibat = [&](Fps& a, int s, int z, int r){
ntt.IButterflyLayered(a.begin(), z, s, r);
};
auto rotbuf = [&](){
std::swap(p,p1); std::swap(p1,p2);
std::swap(q,q1); std::swap(q1,q2);
};
while(true){
int fg = (d <= e ? 1 : 0);
int m = n/2;
for(int t=0; t<2; t++){
if(fg^t){
ibat(q, d, e, 1);
ibat(p, d, e, 1);
if(d == 1) break;
for(int i=0; i<m; i++) q1[i] = q[i];
for(int i=0; i<m; i++) q1[m+i] = Zero;
bat(q1, d, e*2, 1);
for(int i=0; i<m; i++) p1[i] = p[i];
for(int i=0; i<m; i++) p1[m+i] = Zero;
bat(p1, d, e*2, 1);
e *= 2; m *= 2;
} else {
for(int i=0; i<m*2; i+=d*2){
for(int j=0; j<d; j++) q1[i+j] = q[i/2+j];
for(int j=0; j<d; j++) q1[i+d+j] = Zero;
}
for(int i=0; i<m*2; i+=d*2){
p1[i] = Zero;
for(int j=0; j<d; j++) p1[i+j+1] = p[i/2+j];
for(int j=1; j<d; j++) p1[i+d+j] = Zero;
}
bat(q1, 1, d*2, e); bat(p1, 1, d*2, e);
d *= 2; m *= 2;
}
rotbuf();
}
if(d == 1) break;
pcoeff *= Elem(n*2);
rotbuf();
for(int i=0; i<n; i++) q2[n+i] -= One + One;
d /= 2;
for(int i=0; i<n; i++) p1[i] = p2[i*2] * q2[i*2+1] + p2[i*2+1] * q2[i*2];
ibat(p1, 1, d, e);
for(int i=0; i<n; i++) q1[i] = q2[i*2] * q2[i*2+1];
ibat(q1, 1, d, e);
d /= 2;
for(int i=0; i<n; i+=d*2) for(int j=0; j<d; j++) p[i/2+j] = p1[i+j+1];
for(int i=0; i<n; i+=d*2) for(int j=0; j<d; j++) q[i/2+j] = q1[i+j];
q.times(invn);
}
q[0] -= One;
n /= 2;
p = p.reverse().clip(0,maxPower+1).times(pcoeff.inv()).move();
if(f[0].val() != 0) p = p.convolve(q.clip(1,n+1).reverse().set(0,One).inv(n),maxPower+1).move();
return p.getVectorMoved();
}
} // namespace nachia
namespace nachia{
template<class Fps>
Fps CompositionalInverseOfFps(int N, Fps f){
assert(f.getCoeff(0).val() == 0);
if(N <= 1) return Fps(N);
using Elem = typename Fps::ElemTy;
auto t = f[1].inv();
f.times(t);
Fps g = FpsSampleCoefficientOfPowers(f.clip(0,N), Fps(1).set(0,Elem(1)), N-1, N-1);
auto comb = Fps::GetComb(); comb.extend(N);
auto K = Elem(N-1);
for(int i=1; i<N; i++) g[i] *= K * comb.invOf(i);
g = g.reverse(N).pow((-K).inv().val(), N);
for(int i=N-1; i>=1; i--) g[i] = g[i-1];
auto tt = t;
for(int i=1; i<N; i++){ g[i] *= tt; tt *= t; }
g[0] = Elem(0);
return g;
}
} // namespace nachia
#line 495 "etc/fps_nachia.hpp"
namespace nachia{
template<class Modint>
class Comb{
private:
std::vector<Modint> F;
std::vector<Modint> iF;
public:
void extend(int newN){
int prevN = (int)F.size() - 1;
if(prevN >= newN) return;
F.resize(newN+1);
iF.resize(newN+1);
for(int i=prevN+1; i<=newN; i++) F[i] = F[i-1] * Modint::raw(i);
iF[newN] = F[newN].inv();
for(int i=newN; i>prevN; i--) iF[i-1] = iF[i] * Modint::raw(i);
}
Comb(int n = 1){
F.assign(2, Modint(1));
iF.assign(2, Modint(1));
extend(n);
}
Modint factorial(int n) const { return F[n]; }
Modint invFactorial(int n) const { return iF[n]; }
Modint invOf(int n) const { return iF[n] * F[n-1]; }
Modint comb(int n, int r) const {
if(n < 0 || n < r || r < 0) return Modint(0);
return F[n] * iF[r] * iF[n-r];
}
Modint invComb(int n, int r) const {
if(n < 0 || n < r || r < 0) return Modint(0);
return iF[n] * F[r] * F[n-r];
}
Modint perm(int n, int r) const {
if(n < 0 || n < r || r < 0) return Modint(0);
return F[n] * iF[n-r];
}
Modint invPerm(int n, int r) const {
if(n < 0 || n < r || r < 0) return Modint(0);
return iF[n] * F[n-r];
}
Modint operator()(int n, int r) const { return comb(n,r); }
};
} // namespace nachia
namespace nachia {
template<class Elem, class NttInst = Ntt<Elem>>
struct FpsNtt {
public:
using Fps = FpsNtt;
using ElemTy = Elem;
static constexpr unsigned int MOD = Elem::mod();
static constexpr int CONV_THRES = 30;
static const NttInst nttInst;
static const unsigned int zeta = nachia::PrimitiveRoot<MOD>::GetVal();
private:
using u32 = unsigned int;
static Elem ZeroElem() noexcept { return Elem(0); }
static Elem OneElem() noexcept { return Elem(1); }
static Comb<Elem> comb;
std::vector<Elem> a;
int RSZ(int& sz) const { return sz = (sz < 0 ? size() : sz); }
public:
int size() const noexcept { return a.size(); }
Elem& operator[](int x) noexcept { return a[x]; }
const Elem& operator[](int x) const noexcept { return a[x]; }
Elem getCoeff(int x) const noexcept { return (0 <= x && x < size()) ? a[x] : ZeroElem(); }
static Comb<Elem>& GetComb() { return comb; }
static int BestNttSize(int x) noexcept { assert(x); return 1 << MsbIndex(x*2-1); }
Fps move(){ return std::move(*this); }
Fps& set(int i, Elem c){ a[i] = c; return *this; }
Fps& removeLeadingZeros(){
int newsz = size();
while(newsz && a[newsz-1].val() == 0) newsz--;
a.resize(newsz);
if((int)a.capacity() / 4 > newsz) a.shrink_to_fit();
return *this;
}
FpsNtt(){}
FpsNtt(int sz) : a(sz, ZeroElem()) {}
FpsNtt(int sz, Elem e) : a(sz, e) {}
FpsNtt(std::vector<Elem>&& src) : a(std::move(src)) {}
FpsNtt(const std::vector<Elem>& src) : a(src) {}
Fps& ntt() {
capSize(BestNttSize(size()));
nttInst.Butterfly(a.begin(), size());
return *this;
}
Fps& intt() {
nttInst.IButterfly(a.begin(), a.size());
return times(Elem::raw(size()).inv());
}
Fps nttDouble(Fps vanilla) const {
int n = size();
assert(n == (n&-n)); // n is a power of 2
Elem q = Elem::raw(zeta).pow((Elem::mod() - 1) / (n*2));
Elem qq = OneElem();
for(int i=0; i<n; i++){ vanilla[i] *= qq; qq *= q; }
vanilla.ntt();
Fps res = clip(0, n*2);
for(int i=0; i<n; i++) res[n+i] = vanilla[i];
return res;
}
Fps nttDouble() const { return nttDouble(clip().intt().move()); }
// Fps res(resSz);
// for(int j=0; j<resSz-destL && j+srcL < srcR; j++) res[j+destL] = a.getCoeff(j+srcL)
// if srcR is unspecified -> srcR = max(srcL, size());
// if resSz is unspecified -> resSz = destL + srcR - srcL
Fps clip(int srcL, int srcR = -1, int destL = 0, int resSz = -1) const {
srcR = RSZ(srcR);
if(resSz < 0) resSz = destL + srcR - srcL;
int rj = std::min(std::min(srcR, size()) - srcL, resSz - destL);
Fps res(resSz);
for(int j=std::max(0, -srcL); j<rj; j++) res[j+destL] = a[j+srcL];
return res;
}
Fps clip() const { return *this; }
Fps& capSize(int l, int r) {
if(r <= (int)size()) a.resize(r);
if(size() <= l) a.resize(l, ZeroElem());
return *this;
}
Fps& capSize(int z){ a.resize(RSZ(z), ZeroElem()); return *this; }
Fps& times(Elem x){ for(int i=0; i<size(); i++){ a[i] *= x; } return *this; }
Fps& timesFactorial(int z = -1){ comb.extend(RSZ(z)); for(int i=0; i<z; i++){ a[i] *= comb.factorial(i); } return *this; }
Fps& timesInvFactorial(int z = -1){ comb.extend(RSZ(z)); for(int i=0; i<z; i++){ a[i] *= comb.invFactorial(i); } return *this; }
Fps& clrRange(int l, int r){ for(int i=l; i<r; i++){ a[i] = ZeroElem(); } return *this; }
Fps& negate(){ for(auto& e : a){ e = -e; } return *this; }
Fps& mulEach(const Fps& other, int maxi = -1){
maxi = std::min(RSZ(maxi), std::min(size(), other.size()));
for(int i=0; i<maxi; i++) a[i] *= other[i];
return *this;
}
Fps& reverse(int sz = -1){ RSZ(sz); std::reverse(a.begin(), a.begin() + sz); return *this; }
Fps& revRange(int l, int r = -1){ RSZ(r); std::reverse(a.begin() + l, a.begin() + r); return *this; }
static Fps convolution(const Fps& a, const Fps& b, int sz = -1){
if(std::min(a.size(), b.size()) <= CONV_THRES){
if(a.size() > b.size()) return convolution(b, a, sz);
if(sz < 0) sz = std::max(0, a.size() + b.size() - 1);
std::vector<Elem> res(sz);
for(int i=0; i<a.size(); i++) for(int j=0; j<b.size() && i+j<sz; j++) res[i+j] += a[i] * b[j];
return res;
}
int Z = BestNttSize(a.size() + b.size() - 1);
return a.clip(0, Z).ntt().mulEach(b.clip(0, Z).ntt()).intt().capSize(sz).move();
}
Fps convolve(const Fps& r, int sz = -1) const { return convolution(*this, r, sz); }
// 1
// ----- = 1 + f + f^2 + f^3 + ...
// 1-f
Fps powerSum(int sz) const {
RSZ(sz);
if(sz == 0) return {};
int q = std::min(sz, 32);
Fps x = Fps(q).set(0, OneElem()).move();
for(int i=1; i<q; i++) for(int j=1; j<=std::min(i,(int)a.size()-1); j++) x[i] += x[i-j] * a[j];
while(x.size() < sz){
int hN = x.size(), N = hN*2;
Fps a = x.clip(0, N).ntt().move();
Fps b = clip(0, N).ntt().mulEach(a).intt().clrRange(0,hN).ntt().mulEach(a).intt().move();
for(int i=0; i<hN; i++) b[i] = x[i];
std::swap(b, x);
}
return x.capSize(sz).move();
}
Fps inv(int sz = -1) const {
RSZ(sz);
Elem iA0 = a[0].inv();
return clip(0, std::min(sz, size())).times(-iA0).set(0, ZeroElem()).powerSum(sz).times(iA0).move();
}
Fps& difference(){
if(size() == 0) return *this;
for(int i=0; i+1<size(); i++) a[i] = a[i+1] * Elem::raw(i+1);
return capSize(size()-1);
}
Fps& integral(){
if(size() == 0) return capSize(1);
capSize(size()+1);
comb.extend(size());
for(int i=size()-1; i>=1; i--) a[i] = a[i-1] * comb.invOf(i);
return set(0, ZeroElem());
}
Fps log(int sz = -1){
RSZ(sz);
assert(sz != 0);
assert(a[0].val() == 1);
return convolution(inv(sz), clip().difference(), sz-1).integral();
}
Fps exp(int sz = -1){
RSZ(sz);
Fps res = Fps(1).set(0, OneElem());
while(res.size() < sz){
auto z = res.size();
auto tmp = res.capSize(z*2).log().set(0, -OneElem()).move();
for(int i=0; i<z*2 && i<size(); i++) tmp[i] -= a[i];
auto resntt = res.clip().ntt().mulEach(tmp.ntt()).intt().move();
for(int i=z; i<z*2; i++) res[i] = -resntt[i];
}
return res.capSize(0, sz).move();
}
Fps pow(unsigned long long k, int sz = -1){
int n = RSZ(sz);
if(k == 0) return Fps(n).set(0, OneElem()).move();
int ctz = 0;
while(ctz<n && a[ctz].val() == 0) ctz++;
if((unsigned long long)ctz >= (n-1) / k + 1) return Fps(n);
Elem a0 = a[ctz];
return clip(ctz, ctz+n-ctz*k).times(a0.inv()).log().times(Elem(k)).exp().times(a0.pow(k)).clip(0, -1, ctz*k);
}
auto begin(){ return a.begin(); }
auto end(){ return a.end(); }
auto begin() const { return a.begin(); }
auto end() const { return a.end(); }
std::string toString(std::string beg = "[ ", std::string delim = " ", std::string en = " ]") const {
std::string res = beg;
bool f = false;
for(auto x : a){ if(f){ res += delim; } f = true; res += std::to_string(x.val()); }
res += en;
return res;
}
std::vector<Elem> getVectorMoved(){ return std::move(a); }
Fps& operator+=(const Fps& r){
capSize(std::max(size(), r.size()));
for(int i=0; i<r.size(); i++) a[i] += r[i];
return *this;
}
Fps& operator-=(const Fps& r){
capSize(std::max(size(), r.size()));
for(int i=0; i<r.size(); i++) a[i] -= r[i];
return *this;
}
Fps operator+(const Fps& r) const { return (clip(0, std::max(size(), r.size())) += r).move(); }
Fps operator-(const Fps& r) const { return (clip(0, std::max(size(), r.size())) -= r).move(); }
Fps operator-() const { return (clip().negate()).move(); }
Fps operator*(const Fps& r) const { return convolve(r).removeLeadingZeros().move(); }
Fps& operator*=(const Fps& r){ return (*this) = operator*(r); }
Fps& operator*=(Elem m){ return times(m); }
Fps operator*(Elem m) const { return (clip() *= m).move(); }
Elem eval(Elem x) const {
Elem res = 0;
for(int i=size()-1; i>=0; i--) res = res * x + a[i];
return res;
}
};
template<class Elem, class NttInst> Comb<Elem> FpsNtt<Elem, NttInst>::comb;
template<class Elem, class NttInst> const NttInst FpsNtt<Elem, NttInst>::nttInst;
} // namespace nachia
namespace nachia{
template<unsigned int MOD>
struct StaticModint{
private:
using u64 = unsigned long long;
unsigned int x;
public:
using my_type = StaticModint;
template< class Elem >
static Elem safe_mod(Elem x){
if(x < 0){
if(0 <= x+MOD) return x + MOD;
return MOD - ((-(x+MOD)-1) % MOD + 1);
}
return x % MOD;
}
StaticModint() : x(0){}
StaticModint(const my_type& a) : x(a.x){}
StaticModint& operator=(const my_type&) = default;
template< class Elem >
StaticModint(Elem v) : x(safe_mod(v)){}
unsigned int operator*() const noexcept { return x; }
my_type& operator+=(const my_type& r) noexcept { auto t = x + r.x; if(t >= MOD) t -= MOD; x = t; return *this; }
my_type operator+(const my_type& r) const noexcept { my_type res = *this; return res += r; }
my_type& operator-=(const my_type& r) noexcept { auto t = x + MOD - r.x; if(t >= MOD) t -= MOD; x = t; return *this; }
my_type operator-(const my_type& r) const noexcept { my_type res = *this; return res -= r; }
my_type operator-() const noexcept { my_type res = *this; res.x = ((res.x == 0) ? 0 : (MOD - res.x)); return res; }
my_type& operator*=(const my_type& r)noexcept { x = (u64)x * r.x % MOD; return *this; }
my_type operator*(const my_type& r) const noexcept { my_type res = *this; return res *= r; }
my_type pow(unsigned long long i) const noexcept {
my_type a = *this, res = 1;
while(i){ if(i & 1){ res *= a; } a *= a; i >>= 1; }
return res;
}
my_type inv() const { return my_type(ExtGcd(x, MOD).first); }
unsigned int val() const noexcept { return x; }
static constexpr unsigned int mod() { return MOD; }
static my_type raw(unsigned int val) noexcept { auto res = my_type(); res.x = val; return res; }
my_type& operator/=(const my_type& r){ return operator*=(r.inv()); }
my_type operator/(const my_type& r) const { return operator*(r.inv()); }
friend ostream &operator<<(ostream &os, StaticModint a){
return os << a.val();
}
};
} // namespace nachia
namespace nachia{
template<class Fps>
Fps EvaluateOnGeometricSequence(const Fps& a, typename Fps::ElemTy w, int len){
using Elem = typename Fps::ElemTy;
int n = a.size();
int x = std::max(n,len);
if(len == 0) return Fps();
if(w.val() == 0 || a.size() == 0) return Fps(std::vector<Elem>(len, a.getCoeff(0))).set(0,a.eval(1)).move();
int nttsz = Fps::BestNttSize(n+len-1);
Fps iwti(nttsz), wti(nttsz);
iwti[0] = wti[0] = Elem::raw(1);
for(int i=1; i<iwti.size(); i++) iwti[i] = iwti[i-1] * w;
for(int i=1; i<wti.size(); i++) wti[i] = wti[i-1] * iwti[i-1];
iwti[x-1] = wti[x-1].inv();
for(int i=x-1; i>=1; i--) iwti[i-1] = iwti[i] * iwti[i-1];
return a.clip(0, nttsz).mulEach(iwti, n).reverse(n)
.ntt().mulEach(wti.ntt()).intt().clip(n-1, len+n-1).mulEach(iwti, len).move();
}
} // namespace nachia
using mint = nachia::StaticModint<998244353>;
using fps = nachia::FpsNtt<mint>;
#line 5 "sol/ac_noya2.cpp"
int main(){
cin.tie(0)->sync_with_stdio(0);
using ll = long long;
ll n, m; cin >> n >> m;
fps f(n), g(n), h(n);
for (ll i = 0; i < n; i++){
ll x; cin >> x;
f[i] = x;
}
for (ll i = 0; i < n; i++){
ll x; cin >> x;
g[i] = x;
}
for (ll i = 0; i < n; i++){
ll x; cin >> x;
h[i] = x;
}
const mint scale = f[1].pow(m);
h.times(scale);
fps ans = nachia::CompositionOfFps(n, h, g);
for (ll i = 0; i < n; i++){
if (i != 0){
cout << ' ';
}
cout << ans[i].val();
}
cout << '\n';
}