結果
| 問題 |
No.980 Fibonacci Convolution Hard
|
| コンテスト | |
| ユーザー |
 tko919
|
| 提出日時 | 2020-02-02 13:29:29 |
| 言語 | C++14 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
WA
|
| 実行時間 | - |
| コード長 | 8,642 bytes |
| コンパイル時間 | 2,311 ms |
| コンパイル使用メモリ | 201,220 KB |
| 実行使用メモリ | 335,320 KB |
| 最終ジャッジ日時 | 2024-09-18 20:38:51 |
| 合計ジャッジ時間 | 28,143 ms |
|
ジャッジサーバーID （参考情報） |
judge3 / judge1 |
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| ファイルパターン | 結果 |
|---|---|
| other | WA * 17 |
ソースコード
#define _USE_MATH_DEFINES
#include <bits/stdc++.h>
using namespace std;
//template
#define rep(i,a,b) for(int i=(a);i<(b);i++)
#define rrep(i,a,b) for(int i=(a);i>(b);i--)
#define ALL(v) (v).begin(),(v).end()
typedef long long int ll;
const int inf = 0x3fffffff; const ll INF = 0x1fffffffffffffff; const double eps=1e-12;
void tostr(ll x,string& res){while(x)res+=('0'+(x%10)),x/=10; reverse(ALL(res)); return;}
template<class T> inline bool chmax(T& a,T b){ if(a<b){a=b;return 1;}return 0; }
template<class T> inline bool chmin(T& a,T b){ if(a>b){a=b;return 1;}return 0; }
//template end
template<ll mod=1000000007>struct mint {
ll val;
static ll get_mod(){return mod;}
ll inv() const{
ll tmp,a=val,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;
}
mint():val(0){}
mint(ll x):val(x>=0?x%mod:mod+(x%mod)){}
mint pow(ll t){mint res=1,b=*this; while(t){if(t&1)res*=b;b*=b;t>>=1;}return res;}
mint& operator+=(const mint& x){if((val+=x.val)>=mod)val-=mod;return *this;}
mint& operator-=(const mint& x){if((val+=mod-x.val)>=mod)val-=mod; return *this;}
mint& operator*=(const mint& x){val=val*x.val%mod; return *this;}
mint& operator/=(const mint& x){val=val*x.inv()%mod; return *this;}
mint operator+(const mint& x)const{return mint(*this)+=x;}
mint operator-(const mint& x)const{return mint(*this)-=x;}
mint operator*(const mint& x)const{return mint(*this)*=x;}
mint operator/(const mint& x)const{return mint(*this)/=x;}
bool operator==(const mint& x)const{return val==x.val;}
bool operator!=(const mint& x)const{return val!=x.val;}
};
template<ll mod>struct factorial {
using Mint=mint<mod>;
vector<Mint> Fact, Finv;
public:
factorial(int maxx){
Fact.resize(maxx+1),Finv.resize(maxx+1); Fact[0]=Mint(1); rep(i,0,maxx)Fact[i+1]=Fact[i]*(i+1);
Finv[maxx]=Mint(1)/Fact[maxx]; rrep(i,maxx,0)Finv[i-1]=Finv[i]*i;
}
Mint fact(int n,bool inv=0){if(inv)return Finv[n];else return Fact[n];}
Mint nPr(int n,int r){if(n<0||n<r||r<0)return Mint(0);else return Fact[n]*Finv[n-r];}
Mint nCr(int n,int r){if(n<0||n<r||r<0)return Mint(0);else return Fact[n]*Finv[r]*Finv[n-r];}
};
vector<ll> rt,irt;
template<ll mod,ll p>void init(int lg=21){
using Mint=mint<mod>; Mint prt=p;
rt.resize(1<<lg,1); irt.resize(1<<lg,1);
rep(w,0,lg){
int mask=(1<<w)-1,t=Mint(-1).val>>w;
Mint g=prt.pow(t),ig=prt.pow(mod-1-t);
rep(i,0,mask){
rt[mask+i+1]=(g*rt[mask+i]).val;
irt[mask+i+1]=(ig*irt[mask+i]).val;
}
}
}
template<ll mod,ll p>struct FPS{
using Mint=mint<mod>;
vector<Mint> f; Mint prt=p;
FPS():f({1}){}
FPS(int _n):f(_n){}
FPS(vector<Mint> _f):f(_f){}
Mint& operator[](const int i){return f[i];}
Mint eval(Mint x){
Mint res,w=1;
for(Mint v:f)res+=w*v,w*=x; return res;
}
FPS inv()const{
assert(f[0]!=0); int n=f.size();
FPS res(n); res.f[0]=f[0].inv();
for(int k=1;k<n;k<<=1){
FPS g(k*2),h(k*2);
rep(i,0,min(k*2,n))g[i]=f[i]; rep(i,0,k)h[i]=res[i];
g.ntt(); h.ntt(); rep(i,0,k*2)g[i]*=h[i]; g.ntt(1);
rep(i,0,k)g[i]=0,g[i+k]*=-1;
g.ntt(); rep(i,0,k*2)g[i]*=h[i]; g.ntt(1);
rep(i,k,min(k*2,n))res[i]=g[i];
} return res;
}
void ntt(bool inv=0){
int n=f.size(); if(n==1)return;
if(inv){
for(int i=1;i<n;i<<=1){
for(int j=0;j<n;j+=i*2){
rep(k,0,i){
f[i+j+k]*=irt[i*2-1+k];
const Mint tmp=f[j+k]-f[i+j+k];
f[j+k]+=f[i+j+k]; f[i+j+k]=tmp;
}
}
}
Mint mul=Mint(n).inv(); rep(i,0,n)f[i]*=mul;
}else{
for(int i=n>>1;i;i>>=1){
for(int j=0;j<n;j+=i*2){
rep(k,0,i){
const Mint tmp=f[j+k]-f[i+j+k];
f[j+k]+=f[i+j+k]; f[i+j+k]=tmp*rt[i*2-1+k];
}
}
}
}
}
FPS operator+(const FPS& g)const{return FPS(*this)+=g;}
FPS operator-(const FPS& g)const{return FPS(*this)-=g;}
FPS operator*(const FPS& g)const{return FPS(*this)*=g;}
template<class T>FPS operator*(T t)const{return FPS(*this)*=t;}
FPS operator/(const FPS& g)const{return FPS(*this)/=g;}
template<class T>FPS operator/(T t)const{return FPS(*this)/=t;}
FPS operator%(const FPS& g)const{return FPS(*this)%=g;}
FPS& operator+=(FPS g){
if(g.f.size()>f.size())f.resize(g.f.size());
rep(i,0,g.f.size())f[i]+=g[i]; return *this;
}
FPS& operator-=(FPS g){
if(g.f.size()>f.size())f.resize(g.f.size());
rep(i,0,g.f.size())f[i]-=g[i]; return *this;
}
FPS& operator*=(FPS g){
int m=f.size()+g.f.size()-1,n=1; while(n<m)n<<=1;
f.resize(n); g.f.resize(n);
ntt(); g.ntt(); rep(i,0,n)f[i]*=g[i];
ntt(1); f.resize(m); return *this;
}
template<class T>FPS& operator*=(T t){for(Mint x:f)x*=t; return *this;}
FPS& operator/=(FPS g){
if(g.f.size()>f.size())return *this=FPS({0});
reverse(ALL(f)); reverse(ALL(g.f));
int n=f.size()-g.f.size()+1;
f.resize(n); g.f.resize(n); FPS mul=g.inv();
*this*=mul; f.resize(n); reverse(ALL(f)); return *this;
}
template<class T>FPS& operator/=(T t){for(Mint x:f)x/=t; return *this;}
FPS& operator%=(FPS g){
*this-=*this/g*g;
while(!f.empty()&&f.back()==0)f.pop_back();
return *this;
}
FPS sqrt(){
int n=f.size(); FPS res(1); res[0]=1;
for(int k=1;k<n;k<<=1){
FPS ff=*this; res.f.resize(k*2);
res+=ff/res; res/=2;
} res.f.resize(n); return res;
}
FPS diff(){
FPS res=*this; rep(i,0,res.f.size()-1)res[i]=res[i+1]*(i+1);
res.f.pop_back(); return res;
}
FPS inte(){
FPS res=*this; res.f.push_back(0);
rrep(i,res.f.size()-1,0)res[i]=res[i-1]/i;
res[0]=0; return res;
}
FPS log(){
assert(f[0]==1); FPS res=diff()/(*this);
res.f.resize(f.size()-1); res=res.inte(); return res;
}
FPS exp(){
assert(f[0]==0); int m=f.size(),n=1; while(n<m)n<<=1;
f.resize(n); FPS d=diff(),res(n); vector<FPS> pre;
for(int k=n;k;k>>=1){
FPS g=d; g.f.resize(k);
g.ntt(); pre.push_back(g);
}
auto dfs=[&](auto dfs,int l,int r,int dep)->void{
if(r-l==1){if(l>0)res[l]/=l; return;}
int m=(l+r)>>1; dfs(dfs,l,m,dep+1);
FPS g(r-l); rep(i,0,m-l)g[i]=res[l+i];
g.ntt(); rep(i,0,r-l)g[i]*=pre[dep][i]; g.ntt(1);
rep(i,m,r)res[i]+=g[i-l-1]; dfs(dfs,m,r,dep+1);
}; res[0]=1; dfs(dfs,0,n,0); res.f.resize(m); return res;
}
};//need to initialize
using P=pair<ll,ll>;
using M1=mint<1045430273>; using M2=mint<1051721729>; using M3=mint<1053818881>;
template<ll mod=1000000007> vector<ll> optional_convolution(vector<ll> a,vector<ll> b){
using Mint=mint<mod>;
vector<Mint> aa(a.size()),bb(b.size());
rep(i,0,a.size())aa[i]=Mint(a[i]);
rep(i,0,b.size())bb[i]=Mint(b[i]);
vector<ll> vals[3];
vector<M1> a1(a.size()),b1(b.size());
rep(i,0,a.size())a1[i]=M1(a[i]);
rep(i,0,b.size())b1[i]=M1(b[i]);
init<1045430273,3>();
FPS<1045430273,3> x1(a1),y1(b1); x1*=y1;
auto f=x1.f; for(auto v:f)vals[0].push_back(v.val);
vector<M2> a2(a.size()),b2(b.size());
rep(i,0,a.size())a2[i]=M2(a[i]);
rep(i,0,b.size())b2[i]=M2(b[i]);
init<1051721729,6>();
FPS<1051721729,6> x2(a2),y2(b2); x2*=y2;
auto g=x2.f; for(auto v:g)vals[1].push_back(v.val);
vector<M3> a3(a.size()),b3(b.size());
rep(i,0,a.size())a3[i]=M3(a[i]);
rep(i,0,b.size())b3[i]=M3(b[i]);
init<1053818881,7>();
FPS<1053818881,7> x3(a3),y3(b3); x3*=y3;
auto h=x3.f; for(auto v:h)vals[2].push_back(v.val);
int n=vals[0].size(); vector<ll> res(n);
M2 r_12=M2(M1::get_mod()).inv();
M3 r_13=M3(M1::get_mod()).inv();
M3 r_23=M3(M2::get_mod()).inv();
M3 r_1323=r_13*r_23;
Mint w1(M1::get_mod());
Mint w2=w1*Mint(M2::get_mod());
rep(i,0,n){
ll a=vals[0][i];
ll b=(vals[1][i]+M2::get_mod()-a)*r_12.val%M2::get_mod();
ll c=((vals[2][i]+M3::get_mod()-a)*r_1323.val+(M3::get_mod()-b)*r_23.val)%M3::get_mod();
res[i]=(a+b*w1.val+c*w2.val)%mod;
} return res;
}
const int sz=1<<20;
int main(){
int p; scanf("%d",&p);
vector<ll> a(sz);
a[1]=1; rep(i,2,sz)a[i]=a[i-1]*p+a[i-2];
vector<ll> res=optional_convolution(a,a);
int q; scanf("%d",&q);
while(q--){
int x; scanf("%d",&x);
printf("%d\n",res[x-2]);
}
return 0;
}