結果
| 問題 |
No.2513 Power Eraser
|
| コンテスト | |
| ユーザー |
 Taiki0715
|
| 提出日時 | 2024-10-20 13:11:50 |
| 言語 | C++23 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 1,731 ms / 6,000 ms |
| コード長 | 22,669 bytes |
| コンパイル時間 | 6,705 ms |
| コンパイル使用メモリ | 335,276 KB |
| 実行使用メモリ | 15,484 KB |
| 最終ジャッジ日時 | 2024-10-20 13:12:55 |
| 合計ジャッジ時間 | 62,032 ms |
|
ジャッジサーバーID （参考情報） |
judge3 / judge5 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 39 |
ソースコード
#include <bits/stdc++.h>
using namespace std;
#if __has_include(<atcoder/all>)
#include <atcoder/all>
#endif
using ll=long long;
using ull=unsigned long long;
using P=pair<ll,ll>;
template<typename T>using minque=priority_queue<T,vector<T>,greater<T>>;
template<typename T>bool chmax(T &a,const T &b){return (a<b?(a=b,true):false);}
template<typename T>bool chmin(T &a,const T &b){return (a>b?(a=b,true):false);}
template<typename T1,typename T2>istream &operator>>(istream &is,pair<T1,T2>&p){is>>p.first>>p.second;return is;}
template<typename T>istream &operator>>(istream &is,vector<T> &a){for(auto &i:a)is>>i;return is;}
template<typename T1,typename T2>void operator++(pair<T1,T2>&a,int n){a.first++,a.second++;}
template<typename T1,typename T2>void operator--(pair<T1,T2>&a,int n){a.first--,a.second--;}
template<typename T>void operator++(vector<T>&a,int n){for(auto &i:a)i++;}
template<typename T>void operator--(vector<T>&a,int n){for(auto &i:a)i--;}
#define reps(i,a,n) for(int i=(a);i<int(n);i++)
#define rep(i,n) reps(i,0,n)
#define all(x) x.begin(),x.end()
#define pcnt(x) __builtin_popcountll(x)
#define fin(x) return cout<<x<<'\n',static_cast<void>(0)
ll myceil(ll a,ll b){return (a+b-1)/b;}
template<typename T,size_t n,size_t id=0>
auto vec(const int (&d)[n],const T &init=T()){
if constexpr (id<n)return vector(d[id],vec<T,n,id+1>(d,init));
else return init;
}
#ifdef LOCAL
#include<debug.h>
#else
#define debug(...) static_cast<void>(0)
#define debugg(...) static_cast<void>(0)
template<typename T1,typename T2>ostream &operator<<(ostream &os,const pair<T1,T2>&p){os<<p.first<<' '<<p.second;return os;}
#endif
void SOLVE();
int main(){
ios::sync_with_stdio(false);
cin.tie(nullptr);
cout<<fixed<<setprecision(16);
#ifdef LOCAL
clock_t start=clock();
#endif
int testcase=1;
//cin>>testcase;
for(int i=0;i<testcase;i++){
SOLVE();
}
#ifdef LOCAL
cerr<<"time:";
cerr<<(clock()-start)/1000;
cerr<<"ms\n";
#endif
}
constexpr int msb(unsigned int n){return n==0?-1:31-__builtin_clz(n);}
constexpr int msb(int n){return n==0?-1:31-__builtin_clz(n);}
constexpr int msb(unsigned long long n){return n==0?-1:63-__builtin_clzll(n);}
constexpr int msb(long long n){return n==0?-1:63-__builtin_clzll(n);}
constexpr int lsb(unsigned int n){return n==0?-1:__builtin_ctz(n);}
constexpr int lsb(int n){return n==0?-1:__builtin_ctz(n);}
constexpr int lsb(unsigned long long n){return n==0?-1:__builtin_ctzll(n);}
constexpr int lsb(long long n){return n==0?-1:__builtin_ctzll(n);}
constexpr unsigned int floor_pow2(unsigned int n){return n==0?0:1u<<msb(n);}
constexpr int floor_pow2(int n){return n<=0?0:1<<msb(n);}
constexpr unsigned long long floor_pow2(unsigned long long n){return n==0?0:1ull<<msb(n);}
constexpr long long floor_pow2(long long n){return n<=0?0:1ll<<msb(n);}
constexpr unsigned int ceil_pow2(unsigned int n){return n<=1?1:1u<<(msb(n-1)+1);}
constexpr int ceil_pow2(int n){return n<=1?1:1<<(msb(n-1)+1);}
constexpr unsigned long long ceil_pow2(unsigned long long n){return n<=1?1:1ull<<(msb(n-1)+1);}
constexpr long long ceil_pow2(long long n){return n<=1?1:1ll<<(msb(n-1)+1);}
constexpr int pow_mod(int a,int n,int mod){
long long res=1;
while(n){
if(n&1)res=res*a%mod;
a=(long long)a*a%mod;
n>>=1;
}
return res;
}
constexpr int primitive_root_constexpr(int x){
if(x==167772161)return 3;
if(x==469762049)return 3;
if(x==754974721)return 11;
if(x==880803841)return 26;
if(x==998244353)return 3;
if(x==2)return 1;
int x2=x;
int p[20];
int c=0;
x--;
for(int i=2;i*i<=x;i++){
if(x%i==0){
p[c++]=i;
while(x%i==0)x/=i;
}
}
if(x!=1)p[c++]=x;
x=x2;
for(int g=2;;g++){
bool ok=true;
for(int i=0;i<c;i++)if(pow_mod(g,(x-1)/p[i],x)==1){
ok=false;
break;
}
if(ok)return g;
}
}
template<int m>
struct ntt_root{
static constexpr int rank2=lsb(m-1);
static constexpr int g=primitive_root_constexpr(m);
std::array<int,rank2+1>root,invroot;
std::array<int,std::max(0,rank2-1)>rate2,invrate2;
std::array<int,std::max(0,rank2-2)>rate3,invrate3;
constexpr ntt_root(){
root[rank2]=pow_mod(g,m>>rank2,m);
invroot[rank2]=pow_mod(root[rank2],m-2,m);
for(int i=rank2-1;i>=0;i--){
root[i]=(long long)root[i+1]*root[i+1]%m;
invroot[i]=(long long)invroot[i+1]*invroot[i+1]%m;
}
int prod=1,invprod=1;
for(int i=0;i<rank2-1;i++){
rate2[i]=(long long)root[i+2]*prod%m;
invrate2[i]=(long long)invroot[i+2]*invprod%m;
prod=(long long)prod*invroot[i+2]%m;
invprod=(long long)invprod*root[i+2]%m;
}
prod=invprod=1;
for(int i=0;i<rank2-2;i++){
rate3[i]=(long long)root[i+3]*prod%m;
invrate3[i]=(long long)invroot[i+3]*invprod%m;
prod=(long long)prod*invroot[i+3]%m;
invprod=(long long)invprod*root[i+3]%m;
}
}
};
template<typename T>
void dft(std::vector<T>&a){
static constexpr ntt_root<T::mod()>r;
static constexpr unsigned long long mod2=(unsigned long long)T::mod()*T::mod();
int n=a.size();
int h=lsb(n);
int len=0;
while(len<h){
if(h-len==1){
T rot=T::raw(1);
for(int s=0;s<(1<<len);s++){
int of=s*2;
T u=a[of],v=a[of+1]*rot;
a[of]=u+v;
a[of+1]=u-v;
rot*=T::raw(r.rate2[lsb(~(unsigned int)s)]);
}
len++;
}
else{
int p=1<<(h-len-2);
T rot=T::raw(1),imag=T::raw(r.root[2]);
for(int s=0;s<(1<<len);s++){
const unsigned long long rot1=rot.val(),rot2=rot1*rot1%T::mod(),rot3=rot1*rot2%T::mod();
int of=s<<(h-len);
for(int i=0;i<p;i++){
const unsigned long long a0=a[i+of].val(),a1=(unsigned long long)a[i+of+p].val()*rot1,a2=(unsigned long long)a[i+of+p*2].val()*rot2,a3=(unsigned long long)a[i+of+p*3].val()*rot3;
const unsigned long long m=(unsigned long long)T(a1+mod2-a3).val()*imag.val();
const unsigned long long k=mod2-a2;
a[i+of]=a0+a2+a1+a3;
a[i+of+p]=a0+a2+(mod2*2-a1-a3);
a[i+of+p*2]=a0+k+m;
a[i+of+p*3]=a0+k+(mod2-m);
}
rot*=T::raw(r.rate3[lsb(~(unsigned int)s)]);
}
len+=2;
}
}
}
template<typename T>
void idft(std::vector<T>&a){
static constexpr ntt_root<T::mod()>r;
static constexpr unsigned long long mod2=(unsigned long long)T::mod()*T::mod();
int n=a.size();
int h=lsb(n);
int len=h;
while(len){
if(len==1){
int p=1<<(h-1);
for(int i=0;i<p;i++){
T u=a[i],v=a[i+p];
a[i]=u+v;
a[i+p]=u-v;
}
len--;
}
else{
int p=1<<(h-len);
T rot=T::raw(1),imag=T::raw(r.invroot[2]);
for(int s=0;s<(1<<(len-2));s++){
const unsigned long long rot1=rot.val(),rot2=rot1*rot1%T::mod(),rot3=rot1*rot2%T::mod();
int of=s<<(h-len+2);
for(int i=0;i<p;i++){
const unsigned long long a0=a[i+of].val(),a1=a[i+of+p].val(),a2=a[i+of+p*2].val(),a3=a[i+of+p*3].val();
const unsigned long long k=T((T::mod()+a2-a3)*imag.val()).val();
a[i+of]=a0+a1+a2+a3;
a[i+of+p]=(a0+T::mod()-a1+k)*rot1;
a[i+of+p*2]=(a0+a1+T::mod()*2-a2-a3)*rot2;
a[i+of+p*3]=(a0+T::mod()*2-a1-k)*rot3;
}
rot*=T::raw(r.invrate3[lsb(~(unsigned int)s)]);
}
len-=2;
}
}
}
template<typename T>
std::vector<T>ntt_convolution(std::vector<T> a,std::vector<T> b){
int n=a.size(),m=b.size(),s=n+m-1;
if(std::min(n,m)<60){
std::vector<T>ret(s,0);
if(n<m)for(int i=0;i<m;i++)for(int j=0;j<n;j++)ret[i+j]+=a[j]*b[i];
else for(int i=0;i<n;i++)for(int j=0;j<m;j++)ret[i+j]+=a[i]*b[j];
return ret;
}
int z=ceil_pow2(s);
a.resize(z,0);
b.resize(z,0);
dft(a),dft(b);
std::vector<T>c(z);
for(int i=0;i<z;i++)c[i]=a[i]*b[i];
idft(c);
T g=T::raw(z).inv();
for(int i=0;i<s;i++)c[i]*=g;
return {c.begin(),c.begin()+s};
}
template<typename T>
void transposed_dft(std::vector<T>&a){
static constexpr ntt_root<T::mod()>r;
static constexpr unsigned long long mod2=(unsigned long long)T::mod()*T::mod();
int n=a.size();
int h=lsb(n);
int len=h;
while(len){
if(len==1){
int p=1<<(h-1);
T rot=T::raw(1);
for(int i=0;i<p;i++){
T u=a[i],v=a[i+p];
a[i]=u+v;
a[i+p]=(u-v)*rot;
}
len--;
}
else{
int p=1<<(h-len);
T rot=T::raw(1),imag=T::raw(r.root[2]);
for(int s=0;s<(1<<(len-2));s++){
const unsigned long long rot1=rot.val(),rot2=rot1*rot1%T::mod(),rot3=rot1*rot2%T::mod();
int of=s<<(h-len+2);
for(int i=0;i<p;i++){
const unsigned long long a0=a[i+of].val(),a1=a[i+of+p].val(),a2=a[i+of+p*2].val(),a3=a[i+of+p*3].val();
const unsigned long long k=T((T::mod()+a2-a3)*imag.val()).val();
a[i+of]=a0+a1+a2+a3;
a[i+of+p]=(a0+T::mod()-a1+k)*rot1;
a[i+of+p*2]=(a0+a1+T::mod()*2-a2-a3)*rot2;
a[i+of+p*3]=(a0+T::mod()*2-a1-k)*rot3;
}
if(s+1!=1<<(len-2))rot*=T::raw(r.rate3[lsb(~(unsigned int)s)]);
}
len-=2;
}
}
}
template<typename T>
void transposed_idft(std::vector<T>&a){
static constexpr ntt_root<T::mod()>r;
static constexpr unsigned long long mod2=(unsigned long long)T::mod()*T::mod();
int n=a.size();
int h=lsb(n);
int len=0;
while(len<h){
if(h-len==1){
T rot=T::raw(1);
for(int s=0;s<(1<<len);s++){
int of=s*2;
T u=a[of],v=a[of+1]*rot;
a[of]=u+v;
a[of+1]=u-v;
if(s+1!=1<<len)rot*=T::raw(r.invrate2[lsb(~(unsigned int)s)]);
}
len++;
}
else{
int p=1<<(h-len-2);
T rot=T::raw(1),imag=T::raw(r.invroot[2]);
for(int s=0;s<(1<<len);s++){
const unsigned long long rot1=rot.val(),rot2=rot1*rot1%T::mod(),rot3=rot1*rot2%T::mod();
int of=s<<(h-len);
for(int i=0;i<p;i++){
const unsigned long long a0=a[i+of].val(),a1=(unsigned long long)a[i+of+p].val()*rot1,a2=(unsigned long long)a[i+of+p*2].val()*rot2,a3=(unsigned long long)a[i+of+p*3].val()*rot3;
const unsigned long long m=(unsigned long long)T(a1+mod2-a3).val()*imag.val();
const unsigned long long k=mod2-a2;
a[i+of]=a0+a2+a1+a3;
a[i+of+p]=a0+a2+(mod2*2-a1-a3);
a[i+of+p*2]=a0+k+m;
a[i+of+p*3]=a0+k+(mod2-m);
}
if(s+1!=1<<len)rot*=T::raw(r.invrate3[lsb(~(unsigned int)s)]);
}
len+=2;
}
}
}
template<typename T>
void ntt_doubling(std::vector<T>&a){
static constexpr ntt_root<T::mod()>r;
int n=a.size()/2;
std::vector<T>b(a.begin(),a.begin()+n);
idft(b);
T now=T::raw(n).inv(),zeta=T::raw(r.root[msb(n)+1]);
for(int i=0;i<n;i++){
b[i]*=now;
now*=zeta;
}
dft(b);
std::copy(b.begin(),b.end(),a.begin()+n);
}
template<typename T>
void transposed_ntt_doubling(std::vector<T>&a){
static constexpr ntt_root<T::mod()>r;
int n=a.size()/2;
std::vector<T>b(a.begin(),a.begin()+n);
a=std::vector<T>(a.begin()+n,a.end());
transposed_dft(a);
T now=T::raw(n).inv(),zeta=T::raw(r.root[msb(n)+1]);
for(int i=0;i<n;i++)a[i]*=now,now*=zeta;
transposed_idft(a);
for(int i=0;i<n;i++)a[i]+=b[i];
}
#include<type_traits>
template<int m>
struct mod_int{
private:
static constexpr unsigned int umod=static_cast<unsigned int>(m);
using uint=unsigned int;
using mint=mod_int;
uint v;
static_assert(m<uint(1)<<31);
public:
mod_int():v(0){}
template<typename T,std::enable_if_t<std::is_signed_v<T>,std::nullptr_t> =nullptr>
mod_int(T a){
a%=m;
if(a<0)v=a+umod;
else v=a;
}
template<typename T,std::enable_if_t<std::is_unsigned_v<T>,std::nullptr_t> =nullptr>
mod_int(T a):v(a%umod){}
static constexpr mint raw(int a){
mint ret;
ret.v=a;
return ret;
}
inline uint val()const{return this->v;}
static constexpr int mod(){return m;}
inline mint &operator+=(const mint &b){
this->v+=b.v;
if(this->v>=umod)this->v-=umod;
return *this;
}
inline mint &operator-=(const mint &b){
this->v-=b.v;
if(this->v>=umod)this->v+=umod;
return *this;
}
inline mint &operator*=(const mint &b){
this->v=((unsigned long long)this->v*b.v)%umod;
return *this;
}
inline mint &operator/=(const mint &b){
*this*=b.inv();
return *this;
}
inline mint operator+()const{return *this;}
inline mint operator-()const{return mint()-*this;}
friend inline mint operator+(const mint &a,const mint &b){return mint(a)+=b;}
friend inline mint operator-(const mint &a,const mint &b){return mint(a)-=b;}
friend inline mint operator*(const mint &a,const mint &b){return mint(a)*=b;}
friend inline mint operator/(const mint &a,const mint &b){return mint(a)/=b;}
friend inline bool operator==(const mint &a,const mint &b){return a.val()==b.val();}
friend inline bool operator!=(const mint &a,const mint &b){return !(a==b);}
inline mint operator++(int){
mint ret=*this;
*this+=1;
return ret;
}
inline mint operator--(int){
mint ret=*this;
*this-=1;
return ret;
}
mint pow(long long n)const{
mint ret=mint::raw(1),a(*this);
while(n){
if(n&1)ret*=a;
a*=a;
n>>=1;
}
return ret;
}
inline mint inv()const{
assert(this->v!=0);
return pow(m-2);
}
mint sqrt()const{
if(this->val()<=1)return *this;
if constexpr(m%8==1){
mint b=2;
while(b.pow((m-1)/2).val()==1)b++;
int m2=m-1,e=0;
while(m2%2==0)m2>>=1,e++;
mint x=this->pow((m2-1)/2);
mint y=(*this)*x*x;
x*=*this;
mint z=b.pow(m2);
while(y.val()!=1){
int j=0;
mint t=y;
while(t.val()!=1)t*=t,j++;
z=z.pow(1<<(e-j-1));
x*=z;
z*=z;
y*=z;e=j;
}
return x;
}
else if constexpr(m%8==5){
mint ret=this->pow((m+3)/8);
if((ret*ret).val()==this->val())return ret;
else return ret*mint::raw(2).pow((m-1)/4);
}
else{
return this->pow((m+1)/4);
}
}
std::pair<bool,mint> safe_sqrt()const{
if(this->pow((m-1)/2)==1)return std::make_pair(true,this->sqrt());
else return std::make_pair(false,0);
}
friend std::istream &operator>>(std::istream &is,mint &b){
long long a;
is>>a;
b=mint(a);
return is;
}
friend std::ostream &operator<<(std::ostream &os,const mint &b){
os<<b.val();
return os;
}
};
using mint998=mod_int<998244353>;
using mint107=mod_int<1000000007>;
int sqrt_mod(int n,int mod){
if(n<=1)return n;
auto powmod=[&](int a,int b)->int {
ll ret=1;
while(b){
if(b&1)ret=(ret*a)%mod;
a=ll(a)*a%mod;
b>>=1;
}
return ret;
};
if(powmod(n,(mod-1)/2)!=1)return -1;
if(mod%8==1){
int b=2;
while(powmod(b,(mod-1)/2)==1)b++;
int m2=mod-1,e=0;
while(m2%2==0)m2>>=1,e++;
int x=powmod(n,(m2-1)/2);
int y=(ll(n)*x%mod)*x%mod;
x=ll(x)*n%mod;
int z=powmod(b,m2);
while(y!=1){
int j=0;
int t=y;
while(t!=1)t=ll(t)*t%mod,j++;
z=powmod(z,1<<(e-j-1));
x=ll(x)*z%mod;
z=ll(z)*z%mod;
y=ll(y)*z%mod;
e=j;
}
return x;
}
else if(mod%8==5){
int ret=powmod(n,(mod+3)/8);
if(ll(ret)*ret%mod==n)return ret;
else{
ret=(ll(ret)*powmod(2,(mod-1)/4))%mod;
return ret;
}
}
else return powmod(n,(mod+1)/4);
}
template<typename T>
vector<vector<T>>convolution2d(const vector<vector<T>>&a,const vector<vector<T>>&b){
int x=a.size()+b.size()-1,y=a[0].size()+b[0].size()-1;
vector<T>f(a.size()*y),g(b.size()*y);
rep(i,a.size())rep(j,a[i].size())f[i*y+j]=a[i][j];
rep(i,b.size())rep(j,b[i].size())g[i*y+j]=b[i][j];
auto c=ntt_convolution(f,g);
vector<vector<T>>ret(x,vector<T>(y));
rep(i,x)rep(j,y)ret[i][j]=c[i*y+j];
return ret;
}
template<typename T>
vector<T> fps_inv(const vector<T> &a,int deg=-1){
int n=a.size();
if(deg==-1)deg=n;
assert(a[0]!=T(0));
vector<T> ret(deg);
ret[0]=a[0].inv();
for(int m=1;m<deg;m<<=1){
vector<T> f(a.begin(),a.begin()+min(n,m*2));
if(f.size()<m*2)f.resize(m*2,0);
vector<T> g(ret);
f.resize(m*2);
dft(f);
g.resize(m*2);
dft(g);
rep(i,m*2)f[i]*=g[i];
idft(f);
T inv=T::raw(m*2).inv();
rep(i,m)f[i]=0;
reps(i,m,m*2)f[i]*=inv;
dft(f);
rep(i,m*2)f[i]*=g[i];
idft(f);
rep(i,m*2)f[i]*=inv;
reps(i,m,min(deg,m*2))ret[i]-=f[i];
}
return ret;
}
template<typename T>
vector<T> fps_diff(const vector<T>&a){
int n=a.size();
vector<T>b(max(0,n-1));
reps(i,1,n)b[i-1]=a[i]*i;
return b;
}
template<typename T>
vector<T> fps_integral(const vector<T>&a){
int n=a.size();
vector<T>b(n+1);
b[0]=0;
if(n)b[1]=1;
reps(i,2,n+1)b[i]=-b[T::mod()%i]*(T::mod()/i);
rep(i,n)b[i+1]*=a[i];
return b;
}
template<typename T>
vector<T> fps_log(const vector<T>&a,int deg=-1){
int n=a.size();
if(deg==-1)deg=n;
vector<T>b=fps_integral(ntt_convolution(fps_diff(a),fps_inv(a,deg)));
return {b.begin(),b.begin()+deg};
}
template<typename T>
vector<T> fps_exp(const vector<T>&a,int deg=-1){
assert(a.empty()||a[0]==0);
int n=a.size();
if(deg==-1)deg=n;
vector<T>b{1};
for(int m=1;m<deg;m*=2){
vector<T>nxt=fps_log(b,m*2);
rep(i,m*2)nxt[i]*=-1;
rep(i,min(n,m*2))nxt[i]+=a[i];
nxt[0]++;
b=ntt_convolution(b,nxt);
b.resize(m*2);
}
return {b.begin(),b.begin()+deg};
}
template<typename T>
vector<T> fps_pow(vector<T> a,ll k,int deg=-1){
int n=a.size();
if(deg==-1)deg=n;
if(k==0){
vector<T>ret(deg,0);
ret[0]=1;
return ret;
}
int of=0;
while(a[of]==0&&of!=n)of++;
if(of==n)return vector<T>(deg,0);
if(of!=0&&k>=deg)return vector<T>(deg,0);
if(of*k>=deg)return vector<T>(deg,0);
a.erase(a.begin(),a.begin()+of);
n=a.size();
T a0=a[0];
T inv=a[0].inv();
rep(i,n)a[i]*=inv;
vector<T>lg=fps_log(a,deg);
rep(i,deg)lg[i]*=k;
vector<T>ep=fps_exp(lg,deg);
T pw=a0.pow(k);
rep(i,deg)ep[i]*=pw;
vector<T>ret(deg,0);
reps(i,of*k,deg)ret[i]=ep[i-of*k];
return ret;
}
template<typename T>
vector<T>fps_pows(vector<T>f,vector<T>g,int n){
int sz=f.size();
vector<vector<T>>p(sz,vector<T>(2)),q(sz,vector<T>(2));
q[0][0]=1;
rep(i,min<int>(g.size(),sz))p[i][0]=g[i];
rep(i,sz)q[i][1]=-f[i];
int k=sz-1;
while(k){
int x=p.size(),y=p[0].size();
vector<vector<T>>mq(q);
for(int i=1;i<x;i+=2)rep(j,y)mq[i][j]=-mq[i][j];
vector<vector<T>>f=convolution2d(p,mq);
vector<vector<T>>g=convolution2d(q,mq);
p.resize(k/2+1);
q.resize(k/2+1);
if(k&1)rep(i,p.size())p[i]=f[i*2+1];
else rep(i,p.size())p[i]=f[i*2];
rep(i,q.size())q[i]=g[i*2];
rep(i,p.size())if(p[i].size()>n+1)p[i].resize(n+1);
rep(i,q.size())if(q[i].size()>n+1)q[i].resize(n+1);
k>>=1;
}
vector<T>f2(p[0]),g2(q[0]);
vector<T>ret=ntt_convolution(f2,fps_inv(g2));
ret.resize(n+1);
return ret;
}
template<typename T>
vector<T>fps_divmod(vector<T>f,vector<T>g){
if(f.empty())return f;
int n=f.size(),m=g.size();
vector<T>r(f);
reverse(all(f)),reverse(all(g));
vector<T>q=ntt_convolution(f,fps_inv(g,n));
q.resize(max(0,n-m+1));
auto p=ntt_convolution(g,q);
reverse(all(p));
rep(i,min<int>(p.size(),m))r[i]-=p[i];
r.resize(m-1);
while(!r.empty()&&r.back().val()==0)r.pop_back();
return r;
}
template<typename T>
vector<T>fps_sqrt(vector<T>f,int deg=-1){
if(deg==-1)deg=f.size();
int prefix_zero=0;
while(prefix_zero<f.size()&&f[prefix_zero].val()==0)prefix_zero++;
if(prefix_zero==f.size())return vector<T>(deg,0);
if(prefix_zero&1)return vector<T>{};
f.erase(f.begin(),f.begin()+prefix_zero);
prefix_zero/=2;
int sq=sqrt_mod(f[0].val(),T::mod());
if(sq==-1)return vector<T>{};
T inv0=f[0].inv();
rep(i,f.size())f[i]*=inv0;
vector<T>g{1};
debug(f);
T inv2=T::raw(2).inv();
while(g.size()<deg-prefix_zero){
vector<T>fp(f.begin(),f.begin()+min(f.size(),g.size()*2));
fp=ntt_convolution(fp,fps_inv(g,g.size()*2));
vector<T>nxtg(g);
nxtg.resize(g.size()*2);
rep(i,nxtg.size()){
if(i<fp.size())nxtg[i]+=fp[i];
nxtg[i]*=inv2;
}
swap(g,nxtg);
}
g.insert(g.begin(),prefix_zero,0);
g.resize(deg);
rep(i,g.size())g[i]*=sq;
return g;
}
template<typename T>
std::vector<T>fps_middle_product(std::vector<T>a,std::vector<T>b){
assert(a.size()>=b.size());
std::reverse(b.begin(),b.end());
int n=a.size(),m=b.size();
int z=ceil_pow2(n);
a.resize(z,0),b.resize(z,0);
dft(a),dft(b);
for(int i=0;i<z;i++)a[i]*=b[i];
idft(a);
T invz=T(z).inv();
for(int i=m-1;i<n;i++)a[i]*=invz;
return vector<T>(a.begin()+m-1,a.begin()+n);
}
template<typename T>
std::vector<T>multipoint_evaluation(std::vector<T>f,const std::vector<T>&x){
int n=ceil_pow2((int)x.size()),log2n=msb(n);
std::vector<std::vector<T>>f2(log2n+1,std::vector<T>(n*2));
for(int i=0;i<x.size();i++)f2[0][i*2]=-x[i];
for(int i=0;i<log2n;i++){
int b=1<<i;
for(int j=0;j<n*2;j+=b*4){
std::vector<T>l(f2[i].begin()+j,f2[i].begin()+j+b);
std::vector<T>r(f2[i].begin()+j+b*2,f2[i].begin()+j+b*3);
l.resize(b*2,0),r.resize(b*2,0);
ntt_doubling(l),ntt_doubling(r);
for(int k=0;k<b;k++)l[k]++,r[k]++;
for(int k=b;k<b*2;k++)l[k]--,r[k]--;
std::copy(l.begin(),l.end(),f2[i].begin()+j);
std::copy(r.begin(),r.end(),f2[i].begin()+j+b*2);
for(int k=0;k<b*2;k++)f2[i+1][j+k]=l[k]*r[k]-T::raw(1);
}
}
std::vector<T>g(f2[log2n].begin(),f2[log2n].begin()+n);
idft(g);
{
T inv=T::raw(g.size()).inv();
for(int i=0;i<n;i++)g[i]*=inv;
}
g.push_back(T::raw(1));
std::reverse(g.begin(),g.end());
g=fps_inv(g,f.size());
f.resize(f.size()+n-1);
f=fps_middle_product(f,g);
std::reverse(f.begin(),f.end());
transposed_idft(f);
{
T inv=T::raw(f.size()).inv();
for(int i=0;i<f.size();i++)f[i]*=inv;
}
for(int i=log2n-1;i>=0;i--){
std::vector<T>nxtf(n);
int b=1<<i;
for(int j=0;j<n;j+=b*2){
std::vector<T>l(b*2),r(b*2);
for(int k=0;k<b*2;k++)l[k]=f[j+k]*f2[i][j*2+b*2+k],r[k]=f[j+k]*f2[i][j*2+k];
transposed_ntt_doubling(l),transposed_ntt_doubling(r);
for(int k=0;k<b;k++)nxtf[j+k]=l[k],nxtf[j+b+k]=r[k];
}
std::swap(f,nxtf);
}
f.resize(x.size());
return f;
}
using mint=mint998;
void SOLVE(){
int n;
cin>>n;
vector<mint>a(n);
cin>>a;
mint ans=1;
auto dfs=[&](auto self,int l,int r)->vector<mint> {
if(l+1==r)return {a[l],-1};
int mid=(l+r)/2;
vector<mint>pl=self(self,l,mid);
vector<mint>pr=self(self,mid,r);
vector<mint>x(a.begin()+mid,a.begin()+r);
vector<mint>b=multipoint_evaluation(pl,x);
for(auto i:b)ans*=i;
return ntt_convolution(pl,pr);
};
dfs(dfs,0,n);
cout<<ans.val()<<endl;
}