結果
| 問題 | No.2583 Differential Equation (Enhanced version) |
| ユーザー |
 tko919
|
| 提出日時 | 2023-12-13 06:48:34 |
| 言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
AC
|
| 実行時間 | 2,578 ms / 10,000 ms |
| コード長 | 23,468 bytes |
| コンパイル時間 | 3,244 ms |
| コンパイル使用メモリ | 230,832 KB |
| 実行使用メモリ | 32,572 KB |
| 最終ジャッジ日時 | 2024-09-27 05:12:55 |
| 合計ジャッジ時間 | 32,755 ms |
|
ジャッジサーバーID （参考情報） |
judge5 / judge3 |
（要ログイン）
テストケース
テストケース表示| 入力 | 結果 | 実行時間 実行使用メモリ |
|---|---|---|
| testcase_00 | AC | 2 ms
5,248 KB |
| testcase_01 | AC | 2 ms
5,376 KB |
| testcase_02 | AC | 2 ms
5,376 KB |
| testcase_03 | AC | 11 ms
5,376 KB |
| testcase_04 | AC | 6 ms
5,376 KB |
| testcase_05 | AC | 11 ms
5,376 KB |
| testcase_06 | AC | 2 ms
5,376 KB |
| testcase_07 | AC | 9 ms
5,376 KB |
| testcase_08 | AC | 6 ms
5,376 KB |
| testcase_09 | AC | 17 ms
5,376 KB |
| testcase_10 | AC | 7 ms
5,376 KB |
| testcase_11 | AC | 10 ms
5,376 KB |
| testcase_12 | AC | 3 ms
5,376 KB |
| testcase_13 | AC | 1,282 ms
18,260 KB |
| testcase_14 | AC | 170 ms
5,732 KB |
| testcase_15 | AC | 388 ms
8,424 KB |
| testcase_16 | AC | 1,629 ms
22,116 KB |
| testcase_17 | AC | 89 ms
5,376 KB |
| testcase_18 | AC | 786 ms
12,236 KB |
| testcase_19 | AC | 636 ms
11,376 KB |
| testcase_20 | AC | 575 ms
10,464 KB |
| testcase_21 | AC | 7 ms
5,376 KB |
| testcase_22 | AC | 1,371 ms
18,940 KB |
| testcase_23 | AC | 2,562 ms
32,324 KB |
| testcase_24 | AC | 2,537 ms
32,572 KB |
| testcase_25 | AC | 2,578 ms
32,456 KB |
| testcase_26 | AC | 2,530 ms
32,264 KB |
| testcase_27 | AC | 2,509 ms
32,320 KB |
| testcase_28 | AC | 329 ms
7,924 KB |
| testcase_29 | AC | 2,288 ms
31,460 KB |
| testcase_30 | AC | 287 ms
7,112 KB |
| testcase_31 | AC | 3 ms
5,376 KB |
| testcase_32 | AC | 3 ms
5,376 KB |
| testcase_33 | AC | 2 ms
5,376 KB |
| testcase_34 | AC | 2 ms
5,376 KB |
| testcase_35 | AC | 5 ms
5,376 KB |
| testcase_36 | AC | 2 ms
5,376 KB |
| testcase_37 | AC | 5 ms
5,376 KB |
| testcase_38 | AC | 2,517 ms
32,304 KB |
| testcase_39 | AC | 2,510 ms
32,456 KB |
ソースコード
#line 1 "library/Template/template.hpp"
#include <bits/stdc++.h>
using namespace std;
#define rep(i,a,b) for(int i=(int)(a);i<(int)(b);i++)
#define ALL(v) (v).begin(),(v).end()
#define UNIQUE(v) sort(ALL(v)),(v).erase(unique(ALL(v)),(v).end())
#define SZ(v) (int)v.size()
#define MIN(v) *min_element(ALL(v))
#define MAX(v) *max_element(ALL(v))
#define LB(v,x) int(lower_bound(ALL(v),(x))-(v).begin())
#define UB(v,x) int(upper_bound(ALL(v),(x))-(v).begin())
using ll=long long int;
using ull=unsigned long long;
const int inf = 0x3fffffff;
const ll INF = 0x1fffffffffffffff;
template<typename T>inline bool chmax(T& a,T b){if(a<b){a=b;return 1;}return 0;}
template<typename T>inline bool chmin(T& a,T b){if(a>b){a=b;return 1;}return 0;}
template<typename T,typename U>T ceil(T x,U y){assert(y!=0); if(y<0)x=-x,y=-y; return (x>0?(x+y-1)/y:x/y);}
template<typename T,typename U>T floor(T x,U y){assert(y!=0); if(y<0)x=-x,y=-y; return (x>0?x/y:(x-y+1)/y);}
template<typename T>int popcnt(T x){return __builtin_popcountll(x);}
template<typename T>int topbit(T x){return (x==0?-1:63-__builtin_clzll(x));}
template<typename T>int lowbit(T x){return (x==0?-1:__builtin_ctzll(x));}
#line 2 "library/Utility/fastio.hpp"
#include <unistd.h>
class FastIO{
static constexpr int L=1<<16;
char rdbuf[L];
int rdLeft=0,rdRight=0;
inline void reload(){
int len=rdRight-rdLeft;
memmove(rdbuf,rdbuf+rdLeft,len);
rdLeft=0,rdRight=len;
rdRight+=fread(rdbuf+len,1,L-len,stdin);
}
inline bool skip(){
for(;;){
while(rdLeft!=rdRight and rdbuf[rdLeft]<=' ')rdLeft++;
if(rdLeft==rdRight){
reload();
if(rdLeft==rdRight)return false;
}
else break;
}
return true;
}
template<typename T,enable_if_t<is_integral<T>::value,int> =0>inline bool _read(T& x){
if(!skip())return false;
if(rdLeft+20>=rdRight)reload();
bool neg=false;
if(rdbuf[rdLeft]=='-'){
neg=true;
rdLeft++;
}
x=0;
while(rdbuf[rdLeft]>='0' and rdLeft<rdRight){
x=x*10+(neg?-(rdbuf[rdLeft++]^48):(rdbuf[rdLeft++]^48));
}
return true;
}
inline bool _read(__int128_t& x){
if(!skip())return false;
if(rdLeft+40>=rdRight)reload();
bool neg=false;
if(rdbuf[rdLeft]=='-'){
neg=true;
rdLeft++;
}
x=0;
while(rdbuf[rdLeft]>='0' and rdLeft<rdRight){
x=x*10+(neg?-(rdbuf[rdLeft++]^48):(rdbuf[rdLeft++]^48));
}
return true;
}
inline bool _read(__uint128_t& x){
if(!skip())return false;
if(rdLeft+40>=rdRight)reload();
x=0;
while(rdbuf[rdLeft]>='0' and rdLeft<rdRight){
x=x*10+(rdbuf[rdLeft++]^48);
}
return true;
}
template<typename T,enable_if_t<is_floating_point<T>::value,int> =0>inline bool _read(T& x){
if(!skip())return false;
if(rdLeft+20>=rdRight)reload();
bool neg=false;
if(rdbuf[rdLeft]=='-'){
neg=true;
rdLeft++;
}
x=0;
while(rdbuf[rdLeft]>='0' and rdbuf[rdLeft]<='9' and rdLeft<rdRight){
x=x*10+(rdbuf[rdLeft++]^48);
}
if(rdbuf[rdLeft]!='.')return true;
rdLeft++;
T base=.1;
while(rdbuf[rdLeft]>='0' and rdbuf[rdLeft]<='9' and rdLeft<rdRight){
x+=base*(rdbuf[rdLeft++]^48);
base*=.1;
}
if(neg)x=-x;
return true;
}
inline bool _read(char& x){
if(!skip())return false;
if(rdLeft+1>=rdRight)reload();
x=rdbuf[rdLeft++];
return true;
}
inline bool _read(string& x){
if(!skip())return false;
for(;;){
int pos=rdLeft;
while(pos<rdRight and rdbuf[pos]>' ')pos++;
x.append(rdbuf+rdLeft,pos-rdLeft);
if(rdLeft==pos)break;
rdLeft=pos;
if(rdLeft==rdRight)reload();
else break;
}
return true;
}
template<typename T>inline bool _read(vector<T>& v){
for(auto& x:v){
if(!_read(x))return false;
}
return true;
}
char wtbuf[L],tmp[50];
int wtRight=0;
inline void _write(const char& x){
if(wtRight>L-32)flush();
wtbuf[wtRight++]=x;
}
inline void _write(const string& x){
for(auto& c:x)_write(c);
}
template<typename T,enable_if_t<is_integral<T>::value,int> =0>inline void _write(T x){
if(wtRight>L-32)flush();
if(x==0){
_write('0');
return;
}
else if(x<0){
_write('-');
if (__builtin_expect(x == std::numeric_limits<T>::min(), 0)) {
switch (sizeof(x)) {
case 2: _write("32768"); return;
case 4: _write("2147483648"); return;
case 8: _write("9223372036854775808"); return;
}
}
x=-x;
}
int pos=0;
while(x!=0){
tmp[pos++]=char((x%10)|48);
x/=10;
}
rep(i,0,pos)wtbuf[wtRight+i]=tmp[pos-1-i];
wtRight+=pos;
}
inline void _write(__int128_t x){
if(wtRight>L-40)flush();
if(x==0){
_write('0');
return;
}
else if(x<0){
_write('-');
x=-x;
}
int pos=0;
while(x!=0){
tmp[pos++]=char((x%10)|48);
x/=10;
}
rep(i,0,pos)wtbuf[wtRight+i]=tmp[pos-1-i];
wtRight+=pos;
}
inline void _write(__uint128_t x){
if(wtRight>L-40)flush();
if(x==0){
_write('0');
return;
}
int pos=0;
while(x!=0){
tmp[pos++]=char((x%10)|48);
x/=10;
}
rep(i,0,pos)wtbuf[wtRight+i]=tmp[pos-1-i];
wtRight+=pos;
}
inline void _write(double x){
ostringstream oss;
oss << fixed << setprecision(15) << double(x);
string s = oss.str();
_write(s);
}
template<typename T>inline void _write(const vector<T>& v){
rep(i,0,v.size()){
if(i)_write(' ');
_write(v[i]);
}
}
public:
FastIO(){}
~FastIO(){flush();}
inline void read(){}
template <typename Head, typename... Tail>inline void read(Head& head,Tail&... tail){
assert(_read(head));
read(tail...);
}
template<bool ln=true,bool space=false>inline void write(){if(ln)_write('\n');}
template <bool ln=true,bool space=false,typename Head, typename... Tail>inline void write(const Head& head,const Tail&... tail){
_write(head);
write<ln,true>(tail...);
if(space)_write(' ');
}
inline void flush(){
fwrite(wtbuf,1,wtRight,stdout);
wtRight=0;
}
};
/**
* @brief Fast IO
*/
#line 3 "sol.cpp"
#line 2 "library/Math/modint.hpp"
template<int mod=1000000007>struct fp {
int v;
static constexpr int get_mod(){return mod;}
int inv() const{
int tmp,a=v,b=mod,x=1,y=0;
while(b)tmp=a/b,a-=tmp*b,swap(a,b),x-=tmp*y,swap(x,y);
if(x<0){x+=mod;} return x;
}
fp(ll x=0){init(x%mod+mod);}
fp& init(ll x){v=(x<mod?x:x-mod); return *this;}
fp operator-()const{return fp()-*this;}
fp pow(ll t){assert(t>=0); fp res=1,b=*this; while(t){if(t&1)res*=b;b*=b;t>>=1;} return res;}
fp& operator+=(const fp& x){return init(v+x.v);}
fp& operator-=(const fp& x){return init(v+mod-x.v);}
fp& operator*=(const fp& x){v=ll(v)*x.v%mod; return *this;}
fp& operator/=(const fp& x){v=ll(v)*x.inv()%mod; return *this;}
fp operator+(const fp& x)const{return fp(*this)+=x;}
fp operator-(const fp& x)const{return fp(*this)-=x;}
fp operator*(const fp& x)const{return fp(*this)*=x;}
fp operator/(const fp& x)const{return fp(*this)/=x;}
bool operator==(const fp& x)const{return v==x.v;}
bool operator!=(const fp& x)const{return v!=x.v;}
friend istream& operator>>(istream& is,fp& x){return is>>x.v;}
friend ostream& operator<<(ostream& os,const fp& x){return os<<x.v;}
};
template<typename T>T Inv(ll n){
static const int md=T::get_mod();
static vector<T> buf({0,1});
assert(n>0);
n%=md;
while(SZ(buf)<=n){
int k=SZ(buf),q=(md+k-1)/k;
buf.push_back(buf[k*q-md]*q);
}
return buf[n];
}
template<typename T>T Fact(ll n,bool inv=0){
static const int md=T::get_mod();
static vector<T> buf({1,1}),ibuf({1,1});
assert(n>=0 and n<md);
while(SZ(buf)<=n){
buf.push_back(buf.back()*SZ(buf));
ibuf.push_back(ibuf.back()*Inv<T>(SZ(ibuf)));
}
return inv?ibuf[n]:buf[n];
}
template<typename T>T nPr(int n,int r,bool inv=0){if(n<0||n<r||r<0)return 0; return Fact<T>(n,inv)*Fact<T>(n-r,inv^1);}
template<typename T>T nCr(int n,int r,bool inv=0){if(n<0||n<r||r<0)return 0; return Fact<T>(n,inv)*Fact<T>(r,inv^1)*Fact<T>(n-r,inv^1);}
template<typename T>T nHr(int n,int r,bool inv=0){return nCr<T>(n+r-1,r,inv);}
/**
* @brief Modint
*/
#line 2 "library/FPS/fps.hpp"
template<typename T>struct Poly:vector<T>{
Poly(int n=0){this->assign(n,T());}
Poly(const initializer_list<T> f):vector<T>::vector(f){}
Poly(const vector<T>& f){this->assign(ALL(f));}
T eval(const T& x){
T res;
for(int i=this->size()-1;i>=0;i--)res*=x,res+=this->at(i);
return res;
}
Poly rev()const{Poly res=*this; reverse(ALL(res)); return res;}
void shrink(){while(!this->empty() and this->back()==0)this->pop_back();}
Poly operator>>(int sz)const{
if((int)this->size()<=sz)return {};
Poly ret(*this);
ret.erase(ret.begin(),ret.begin()+sz);
return ret;
}
Poly operator<<(int sz)const{
Poly ret(*this);
ret.insert(ret.begin(),sz,T(0));
return ret;
}
vector<T> mult(const vector<T>& a,const vector<T>& b,bool same=0)const{
if(a.empty() or b.empty())return vector<T>();
int n=a.size()+b.size()-1,m=1<<__lg(n*2-1);
vector<T> res(m);
rep(i,0,a.size())res[i]=a[i];
NTT(res,0);
if(same)rep(i,0,m)res[i]*=res[i];
else{
vector<T> c(m);
rep(i,0,b.size())c[i]=b[i];
NTT(c,0);
rep(i,0,m)res[i]*=c[i];
}
NTT(res,1);
res.resize(n);
return res;
}
Poly square()const{return Poly(mult(*this,*this,1));}
Poly operator-()const{return Poly()-*this;}
Poly operator+(const Poly& g)const{return Poly(*this)+=g;}
Poly operator+(const T& g)const{return Poly(*this)+=g;}
Poly operator-(const Poly& g)const{return Poly(*this)-=g;}
Poly operator-(const T& g)const{return Poly(*this)-=g;}
Poly operator*(const Poly& g)const{return Poly(*this)*=g;}
Poly operator*(const T& g)const{return Poly(*this)*=g;}
Poly operator/(const Poly& g)const{return Poly(*this)/=g;}
Poly operator/(const T& g)const{return Poly(*this)/=g;}
Poly operator%(const Poly& g)const{return Poly(*this)%=g;}
pair<Poly,Poly> divmod(const Poly& g)const{
Poly q=*this/g,r=*this-g*q;
r.shrink();
return {q,r};
}
Poly& operator+=(const Poly& g){
if(g.size()>this->size())this->resize(g.size());
rep(i,0,g.size()){(*this)[i]+=g[i];} return *this;
}
Poly& operator+=(const T& g){
if(this->empty())this->push_back(0);
(*this)[0]+=g; return *this;
}
Poly& operator-=(const Poly& g){
if(g.size()>this->size())this->resize(g.size());
rep(i,0,g.size()){(*this)[i]-=g[i];} return *this;
}
Poly& operator-=(const T& g){
if(this->empty())this->push_back(0);
(*this)[0]-=g; return *this;
}
Poly& operator*=(const Poly& g){
*this=mult(*this,g,0);
return *this;
}
Poly& operator*=(const T& g){
rep(i,0,this->size())(*this)[i]*=g;
return *this;
}
Poly& operator/=(const Poly& g){
if(g.size()>this->size()){
this->clear(); return *this;
}
Poly g2=g;
reverse(ALL(*this));
reverse(ALL(g2));
int n=this->size()-g2.size()+1;
this->resize(n); g2.resize(n);
*this*=g2.inv(); this->resize(n);
reverse(ALL(*this));
shrink();
return *this;
}
Poly& operator/=(const T& g){
rep(i,0,this->size())(*this)[i]/=g;
return *this;
}
Poly& operator%=(const Poly& g){*this-=*this/g*g; shrink(); return *this;}
Poly diff()const{
Poly res(this->size()-1);
rep(i,0,res.size())res[i]=(*this)[i+1]*(i+1);
return res;
}
Poly inte()const{
Poly res(this->size()+1);
for(int i=res.size()-1;i;i--)res[i]=(*this)[i-1]/i;
return res;
}
Poly log()const{
assert(this->front()==1); const int n=this->size();
Poly res=diff()*inv(); res=res.inte();
res.resize(n); return res;
}
Poly shift(const int& c)const{
const int n=this->size();
Poly res=*this,g(n); g[0]=1; rep(i,1,n)g[i]=g[i-1]*c/i;
vector<T> fact(n,1);
rep(i,0,n){
if(i)fact[i]=fact[i-1]*i;
res[i]*=fact[i];
}
res=res.rev();
res*=g;
res.resize(n);
res=res.rev();
rep(i,0,n)res[i]/=fact[i];
return res;
}
Poly inv()const{
const int n=this->size();
Poly res(1); res.front()=T(1)/this->front();
for(int k=1;k<n;k<<=1){
Poly f(k*2),g(k*2);
rep(i,0,min(n,k*2))f[i]=(*this)[i];
rep(i,0,k)g[i]=res[i];
NTT(f,0);
NTT(g,0);
rep(i,0,k*2)f[i]*=g[i];
NTT(f,1);
rep(i,0,k){f[i]=0; f[i+k]=-f[i+k];}
NTT(f,0);
rep(i,0,k*2)f[i]*=g[i];
NTT(f,1);
rep(i,0,k)f[i]=res[i];
swap(res,f);
} res.resize(n); return res;
}
Poly exp()const{
const int n=this->size();
if(n==1)return Poly({T(1)});
Poly b(2),c(1),z1,z2(2);
b[0]=c[0]=z2[0]=z2[1]=1; b[1]=(*this)[1];
for(int k=2;k<n;k<<=1){
Poly y=b;
y.resize(k*2);
NTT(y,0);
z1=z2;
Poly z(k);
rep(i,0,k)z[i]=y[i]*z1[i];
NTT(z,1);
rep(i,0,k>>1)z[i]=0;
NTT(z,0);
rep(i,0,k)z[i]*=-z1[i];
NTT(z,1);
c.insert(c.end(),z.begin()+(k>>1),z.end());
z2=c;
z2.resize(k*2);
NTT(z2,0);
Poly x=*this;
x.resize(k);
x=x.diff();x.resize(k);
NTT(x,0);
rep(i,0,k)x[i]*=y[i];
NTT(x,1);
Poly bb=b.diff();
rep(i,0,k-1)x[i]-=bb[i];
x.resize(k*2);
rep(i,0,k-1){x[k+i]=x[i]; x[i]=0;}
NTT(x,0);
rep(i,0,k*2)x[i]*=z2[i];
NTT(x,1);
x.pop_back();
x=x.inte();
rep(i,k,min(n,k*2))x[i]+=(*this)[i];
rep(i,0,k)x[i]=0;
NTT(x,0);
rep(i,0,k*2)x[i]*=y[i];
NTT(x,1);
b.insert(b.end(),x.begin()+k,x.end());
} b.resize(n); return b;
}
Poly pow(ll t){
if(t==0){
Poly res(this->size()); res[0]=1;
return res;
}
int n=this->size(),k=0; while(k<n and (*this)[k]==0)k++;
Poly res(n); if(__int128_t(t)*k>=n)return res;
n-=t*k; Poly g(n); T c=(*this)[k],ic=c.inv();
rep(i,0,n)g[i]=(*this)[i+k]*ic;
g=g.log(); for(auto& x:g)x*=t; g=g.exp();
c=c.pow(t); rep(i,0,n)res[i+t*k]=g[i]*c; return res;
}
void NTT(vector<T>& a,bool inv)const;
};
/**
* @brief Formal Power Series (NTT-friendly mod)
*/
#line 6 "sol.cpp"
using Fp=fp<998244353>;
template <typename Mint> struct NTT {
static vector<Mint> roots, iroots, rate3, irate3;
static int max_base;
NTT() = default;
static void init() {
if (roots.empty()) {
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++;
Mint root = 2;
while (root.pow((mod - 1) >> 1) == 1) {
root += 1;
}
assert(root.pow(mod - 1) == 1);
roots.resize(max_base + 1);
iroots.resize(max_base + 1);
rate3.resize(max_base + 1);
irate3.resize(max_base + 1);
roots[max_base] = root.pow((mod - 1) >> max_base);
iroots[max_base] = Mint(1) / roots[max_base];
for (int i = max_base - 1; i >= 0; i--) {
roots[i] = roots[i + 1] * roots[i + 1];
iroots[i] = iroots[i + 1] * iroots[i + 1];
}
{
Mint prod = 1, iprod = 1;
for (int i = 0; i <= max_base - 3; i++) {
rate3[i] = roots[i + 3] * prod;
irate3[i] = iroots[i + 3] * iprod;
prod *= iroots[i + 3];
iprod *= roots[i + 3];
}
}
}
}
static void ntt(vector<Mint> &a) {
init();
const int n = (int)a.size();
assert((n & (n - 1)) == 0);
int h = __builtin_ctz(n);
assert(h <= max_base);
int len = 0;
Mint imag = roots[2];
if (h & 1) {
int p = 1 << (h - 1);
Mint rot = 1;
for (int i = 0; i < p; i++) {
auto r = a[i + p];
a[i + p] = a[i] - r;
a[i] += r;
}
len++;
}
for (; len + 1 < h; len += 2) {
int p = 1 << (h - len - 2);
{ // s = 0
for (int i = 0; i < p; i++) {
auto a0 = a[i];
auto a1 = a[i + p];
auto a2 = a[i + 2 * p];
auto a3 = a[i + 3 * p];
auto a1na3imag = (a1 - a3) * imag;
auto a0a2 = a0 + a2;
auto a1a3 = a1 + a3;
auto a0na2 = a0 - a2;
a[i] = a0a2 + a1a3;
a[i + 1 * p] = a0a2 - a1a3;
a[i + 2 * p] = a0na2 + a1na3imag;
a[i + 3 * p] = a0na2 - a1na3imag;
}
}
Mint rot = rate3[0];
for (int s = 1; s < (1 << len); s++) {
int offset = s << (h - len);
Mint rot2 = rot * rot;
Mint rot3 = rot2 * rot;
for (int i = 0; i < p; i++) {
auto a0 = a[i + offset];
auto a1 = a[i + offset + p] * rot;
auto a2 = a[i + offset + 2 * p] * rot2;
auto a3 = a[i + offset + 3 * p] * rot3;
auto a1na3imag = (a1 - a3) * imag;
auto a0a2 = a0 + a2;
auto a1a3 = a1 + a3;
auto a0na2 = a0 - a2;
a[i + offset] = a0a2 + a1a3;
a[i + offset + 1 * p] = a0a2 - a1a3;
a[i + offset + 2 * p] = a0na2 + a1na3imag;
a[i + offset + 3 * p] = a0na2 - a1na3imag;
}
rot *= rate3[__builtin_ctz(~s)];
}
}
}
static void intt(vector<Mint> &a, bool f = true) {
init();
const int n = (int)a.size();
assert((n & (n - 1)) == 0);
int h = __builtin_ctz(n);
assert(h <= max_base);
int len = h;
Mint iimag = iroots[2];
for (; len > 1; len -= 2) {
int p = 1 << (h - len);
{ // s = 0
for (int i = 0; i < p; i++) {
auto a0 = a[i];
auto a1 = a[i + 1 * p];
auto a2 = a[i + 2 * p];
auto a3 = a[i + 3 * p];
auto a2na3iimag = (a2 - a3) * iimag;
auto a0na1 = a0 - a1;
auto a0a1 = a0 + a1;
auto a2a3 = a2 + a3;
a[i] = a0a1 + a2a3;
a[i + 1 * p] = (a0na1 + a2na3iimag);
a[i + 2 * p] = (a0a1 - a2a3);
a[i + 3 * p] = (a0na1 - a2na3iimag);
}
}
Mint irot = irate3[0];
for (int s = 1; s < (1 << (len - 2)); s++) {
int offset = s << (h - len + 2);
Mint irot2 = irot * irot;
Mint irot3 = irot2 * irot;
for (int i = 0; i < p; i++) {
auto a0 = a[i + offset];
auto a1 = a[i + offset + 1 * p];
auto a2 = a[i + offset + 2 * p];
auto a3 = a[i + offset + 3 * p];
auto a2na3iimag = (a2 - a3) * iimag;
auto a0na1 = a0 - a1;
auto a0a1 = a0 + a1;
auto a2a3 = a2 + a3;
a[i + offset] = a0a1 + a2a3;
a[i + offset + 1 * p] = (a0na1 + a2na3iimag) * irot;
a[i + offset + 2 * p] = (a0a1 - a2a3) * irot2;
a[i + offset + 3 * p] = (a0na1 - a2na3iimag) * irot3;
}
irot *= irate3[__builtin_ctz(~s)];
}
}
if (len >= 1) {
int p = 1 << (h - 1);
for (int i = 0; i < p; i++) {
auto ajp = a[i] - a[i + p];
a[i] += a[i + p];
a[i + p] = ajp;
}
}
if (f) {
Mint inv_sz = Mint(1) / n;
for (int i = 0; i < n; i++)
a[i] *= inv_sz;
}
}
static vector<Mint> mult(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>NTT<Mint>::roots = vector<Mint>();
template <typename Mint>
vector<Mint>NTT<Mint>::iroots = vector<Mint>();
template <typename Mint>
vector<Mint>NTT<Mint>::rate3 = vector<Mint>();
template <typename Mint>
vector<Mint>NTT<Mint>::irate3 = vector<Mint>();
template <typename Mint>
int NTT<Mint>::max_base = 0;
NTT<Fp> ntt;
template<>void Poly<Fp>::NTT(vector<Fp>& v,bool inv)const{return inv?ntt.intt(v):ntt.ntt(v);}
template<typename T>Poly<T> comp_ApBx(const Poly<T>& f,T a,T b){ // f(a+bx)
auto g=f.shift(a.v);
T pw=1;
for(auto& x:g){
x*=pw;
pw*=b;
}
return g;
}
template<typename T>Poly<T> Mobius(const Poly<T>& f,T a,T b,T c,T d){ // f((a+bx)/(c+dx))
assert(c!=0 or d!=0);
if(d==0){
T a_c=a/c,b_c=b/c;
return comp_ApBx(f,a_c,b_c);
}
T p=b/d,q=a-b*c/d;
auto g=comp_ApBx(f,p,q);
reverse(ALL(g));
g=comp_ApBx(g,c,d);
int n=g.size();
Poly<T> den(n);
T cpw=c.pow(n-1),dpw=1,cinv=c.inv();
rep(i,0,n){
den[i]=cpw*dpw*nCr<T>(n-1,i);
cpw*=cinv,dpw*=d;
}
g*=den.inv();
g.resize(n);
return g;
}
FastIO io;
int main(){
int n,m;
io.read(n,m);
Poly<Fp> a(m);
rep(i,0,m)io.read(a[i].v);
a.resize(n*2);
rep(i,2,SZ(a))a[i]+=a[i-2];
rep(i,0,SZ(a))a[i]=-a[i];
a=a.inte().exp();
auto F0=a<<1;
F0.resize(n*3+2);
auto G0=Mobius<Fp>(F0,1,-1,1,1);
rep(i,0,SZ(G0))G0[i]*=Fp(i*2).pow(n);
auto Gn=Mobius<Fp>(G0,0,-1,2,1);
Gn=Gn.shift(-1);
auto Fn=Gn*a.inv();
Fn.resize(n+2);
rep(i,0,n+2)io.write<false,true>(Fn[i].v);
io.write();
return 0;
}