結果

問題 No.980 Fibonacci Convolution Hard
ユーザー tko919tko919
提出日時 2020-02-02 13:47:49
言語 C++14
(gcc 12.3.0 + boost 1.83.0)
結果
WA  
実行時間 -
コード長 8,695 bytes
コンパイル時間 2,654 ms
コンパイル使用メモリ 200,976 KB
実行使用メモリ 335,212 KB
最終ジャッジ日時 2023-10-19 00:48:05
合計ジャッジ時間 31,871 ms
ジャッジサーバーID
（参考情報） 		judge11 / judge15
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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 WA -
testcase_01 WA -
testcase_02 WA -
testcase_03 WA -
testcase_04 WA -
testcase_05 WA -
testcase_06 WA -
testcase_07 WA -
testcase_08 WA -
testcase_09 WA -
testcase_10 WA -
testcase_11 WA -
testcase_12 WA -
testcase_13 WA -
testcase_14 WA -
testcase_15 WA -
testcase_16 WA -
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ソースコード

diff # 

#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;
vector<ll> a,res;

int main(){
   int p; scanf("%d",&p);
   a.resize(sz);
   a[0]=0; a[1]=1; rep(i,2,sz)a[i]=mint<>(a[i-1]*p+a[i-2]).val;
   res=optional_convolution(a,a);
   printf("%d\n",res.size());
   int q; scanf("%d",&q);
   while(q--){
      int x; scanf("%d",&x);
      printf("%d\n",res[x-2]);
   }
   return 0;
}
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