結果
| 問題 | No.980 Fibonacci Convolution Hard |
| ユーザー |
 smiken_61
|
| 提出日時 | 2022-02-27 23:56:57 |
| 言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
AC
|
| 実行時間 | 1,157 ms / 2,000 ms |
| コード長 | 12,119 bytes |
| コンパイル時間 | 4,874 ms |
| コンパイル使用メモリ | 277,892 KB |
| 実行使用メモリ | 6,944 KB |
| 最終ジャッジ日時 | 2024-07-06 02:48:25 |
| 合計ジャッジ時間 | 27,524 ms |
|
ジャッジサーバーID （参考情報） |
judge1 / judge3 |
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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 | AC | 1,099 ms
6,812 KB |
| testcase_01 | AC | 1,103 ms
6,940 KB |
| testcase_02 | AC | 1,109 ms
6,944 KB |
| testcase_03 | AC | 1,157 ms
6,940 KB |
| testcase_04 | AC | 1,148 ms
6,944 KB |
| testcase_05 | AC | 1,116 ms
6,940 KB |
| testcase_06 | AC | 1,121 ms
6,944 KB |
| testcase_07 | AC | 1,107 ms
6,944 KB |
| testcase_08 | AC | 1,109 ms
6,944 KB |
| testcase_09 | AC | 1,091 ms
6,940 KB |
| testcase_10 | AC | 1,130 ms
6,944 KB |
| testcase_11 | AC | 1,126 ms
6,940 KB |
| testcase_12 | AC | 1,134 ms
6,944 KB |
| testcase_13 | AC | 1,123 ms
6,940 KB |
| testcase_14 | AC | 1,138 ms
6,940 KB |
| testcase_15 | AC | 1,113 ms
6,944 KB |
| testcase_16 | AC | 1,038 ms
6,940 KB |
ソースコード
#include <bits/stdc++.h>
#include <atcoder/all>
using namespace atcoder;
// tabaicho see https://boostjp.github.io/tips/multiprec-int.html
// #include <boost/multiprecision/cpp_int.hpp>
// using namespace boost::multiprecision;
// cpp_int
// int128_t
// int256_t
// int512_t
// int1024_t
// uint128_t
// uint256_t
// uint512_t
// uint1024_t
#define int long long
#define inf 1000000007
// #define inf 998244353
#define pa pair<int,int>
#define ppa pair<pa,pa>
#define ll long long
#define PI 3.14159265358979323846
#define mp make_pair
#define pb push_back
#define EPS (1e-8)
using namespace std;
int dx[8]={0,1,0,-1,1,1,-1,-1};
int dy[8]={1,0,-1,0,-1,1,1,-1};
class pa3{
public:
int x;
int y,z;
pa3(int x=0,int y=0,int z=0):x(x),y(y),z(z) {}
bool operator < (const pa3 &p) const{
if(x!=p.x) return x<p.x;
if(y!=p.y) return y<p.y;
return z<p.z;
//return x != p.x ? x<p.x: y<p.y;
}
bool operator > (const pa3 &p) const{
if(x!=p.x) return x>p.x;
if(y!=p.y) return y>p.y;
return z>p.z;
//return x != p.x ? x<p.x: y<p.y;
}
bool operator == (const pa3 &p) const{
return x==p.x && y==p.y && z==p.z;
}
bool operator != (const pa3 &p) const{
return !( x==p.x && y==p.y && z==p.z);
}
};
class pa4{
public:
int x;
int y,z,w;
pa4(int x=0,int y=0,int z=0,int w=0):x(x),y(y),z(z),w(w) {}
bool operator < (const pa4 &p) const{
if(x!=p.x) return x<p.x;
if(y!=p.y) return y<p.y;
if(z!=p.z)return z<p.z;
return w<p.w;
//return x != p.x ? x<p.x: y<p.y;
}
bool operator > (const pa4 &p) const{
if(x!=p.x) return x>p.x;
if(y!=p.y) return y>p.y;
if(z!=p.z)return z>p.z;
return w>p.w;
//return x != p.x ? x<p.x: y<p.y;
}
bool operator == (const pa4 &p) const{
return x==p.x && y==p.y && z==p.z &&w==p.w;
}
};
class pa2{
public:
int x,y;
pa2(int x=0,int y=0):x(x),y(y) {}
pa2 operator + (pa2 p) {return pa2(x+p.x,y+p.y);}
pa2 operator - (pa2 p) {return pa2(x-p.x,y-p.y);}
bool operator < (const pa2 &p) const{
return y != p.y ? y<p.y: x<p.x;
}
bool operator > (const pa2 &p) const{
return x != p.x ? x<p.x: y<p.y;
}
bool operator == (const pa2 &p) const{
return abs(x-p.x)==0 && abs(y-p.y)==0;
}
bool operator != (const pa2 &p) const{
return !(abs(x-p.x)==0 && abs(y-p.y)==0);
}
};
string itos( int i ) {
ostringstream s ;
s << i ;
return s.str() ;
}
int Gcd(int v,int b){
if(v==0) return b;
if(b==0) return v;
if(v>b) return Gcd(b,v);
if(v==b) return b;
if(b%v==0) return v;
return Gcd(v,b%v);
}
int extgcd(int a, int b, int &x, int &y) {
if (b == 0) {
x = 1;
y = 0;
return a;
}
int d = extgcd(b, a%b, y, x);
y -= a/b * x;
return d;
}
pa operator+(const pa & l,const pa & r) {
return {l.first+r.first,l.second+r.second};
}
pa operator-(const pa & l,const pa & r) {
return {l.first-r.first,l.second-r.second};
}
pair<double,double> operator-(const pair<double,double> & l,const pair<double,double> & r) {
return {l.first-r.first,l.second-r.second};
}
ostream& operator<<(ostream& os, const vector<int>& VEC){
for(auto v:VEC)os<<v<<" ";
return os;
}
ostream& operator<<(ostream& os, const pair<double,double>& PAI){
os<<PAI.first<<" : "<<PAI.second;
return os;
}
ostream& operator<<(ostream& os, const pa& PAI){
os<<PAI.first<<" : "<<PAI.second;
return os;
}
ostream& operator<<(ostream& os, const pa3& PAI){
os<<PAI.x<<" : "<<PAI.y<<" : "<<PAI.z;
return os;
}
ostream& operator<<(ostream& os, const pa4& PAI){
os<<PAI.x<<" : "<<PAI.y<<" : "<<PAI.z<<" : "<<PAI.w;
return os;
}
ostream& operator<<(ostream& os, const vector<pa>& VEC){
for(auto v:VEC)os<<v<<" ";
return os;
}
ostream& operator<<(ostream& os, const vector<pa3>& VEC){
for(auto v:VEC){
os<<v<<" ";
os<<endl;
}
return os;
}
int beki(int wa,ll rr,int warukazu){
if(rr==0) return 1%warukazu;
if(rr==1) return wa%warukazu;
wa%=warukazu;
if(rr%2==1) return ((ll)beki(wa,rr-1,warukazu)*(ll)wa)%warukazu;
ll zx=beki(wa,rr/2,warukazu);
return (zx*zx)%warukazu;
}
int pr[2500002];
int inv[2500002];
//const int mod=998244353;
const int mod=1000000007;
int comb(int nn,int rr){
if(nn==-1&&rr==-1)return 1;
if(rr<0 || rr>nn || nn<0) return 0;
int r=pr[nn]*inv[rr];
r%=mod;
r*=inv[nn-rr];
r%=mod;
return r;
}
void gya(int ert){
pr[0]=1;
for(int i=1;i<=ert;i++){
pr[i]=((ll)pr[i-1]*i)%mod;
}
inv[ert]=beki(pr[ert],mod-2,mod);
for(int i=ert-1;i>=0;i--){
inv[i]=(ll)inv[i+1]*(i+1)%mod;
}
}
int beki(int a,int b){
int ANS=1;
int be=a%mod;
while(b){
if(b&1){
ANS*=be;
ANS%=mod;
}
be*=be;
be%=mod;
b/=2;
}
return ANS;
}
// cin.tie(0);
// ios::sync_with_stdio(false);
//priority_queue<pa3,vector<pa3>,greater<pa3>> pq;
//sort(ve.begin(),ve.end(),greater<int>());
// mt19937(clock_per_sec);
// mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count()) ;
// a,b,c : positive int a*b<=c <=> a<=c/b
// auto dfs=[&](auto &&self,int r,int p)->int{
// };
class Point{
public:
double x,y;
Point(double x=0,double y=0):x(x),y(y) {}
Point operator + (Point p) {return Point(x+p.x,y+p.y);}
Point operator - (Point p) {return Point(x-p.x,y-p.y);}
Point operator * (double a) {return Point(x*a,y*a);}
Point operator / (double a) {return Point(x/a,y/a);}
double absv() {return sqrt(norm());}
double norm() {return x*x+y*y;}
bool operator < (const Point &p) const{
return x != p.x ? x<p.x: y<p.y;
}
bool operator == (const Point &p) const{
return fabs(x-p.x)<EPS && fabs(y-p.y)<EPS;
}
};
class Line{
public:
// y=ax+b
double a;
double b;
Line(double a=0,double b=0):a(a),b(b) {}
double eval(double x){return a*x+b;}
bool operator < (const Line &p) const{
return abs(a-p.a)>EPS ? a<p.a: b<p.b;
}
};
Point intersect_line(Line A,Line B){
double x=(B.b-A.b)/(A.a-B.a);
return Point(x,A.eval(x));
}
Line line_from_2_Point(Point A,Point B){
// line which through A,B
double a=(B.y-A.y)/(B.x-A.x);
return Line(a,A.y-a*A.x);
}
struct Segmin{
// 1
// 2 3
// 4 5 6 7
private:
public:
// (1<<15)=32768
// 1<<16 = 65536
// 1<<17 = 131072
// 1<<18 = 262144
int cor=(1<<19);
vector<pa> vec;
void shoki1(){
vec.resize(2*cor+3, mp(inf*2000000000ll*2ll,0));
for(int i=cor;i<2*cor;i++)vec[i].second=i-cor;
}
void shoki2(){
for(int i=cor-1;i>0;i--) {
if(vec[2*i].first<=vec[2*i+1].first) vec[i]=vec[2*i];
else vec[i]=vec[2*i+1];
}
}
void updadd(int x,int w){
//x 項目に w加算
x+=cor;
vec[x].first+=w;
x/=2;
while(x){
if(vec[2*x].first<=vec[2*x+1].first) vec[x]=vec[2*x];
else vec[x]=vec[2*x+1];
x/=2;
}
}
void updchan(int x,int w){
//x項目をwに変更
x+=cor;
vec[x].first=w;
x/=2;
while(x){
if(vec[2*x].first<=vec[2*x+1].first) vec[x]=vec[2*x];
else vec[x]=vec[2*x+1];
x/=2;
}
}
// [a,b)
// k-th node
// k no kukanha [l,r)
pa segmin(int a,int b){
a+=cor;
b+=cor;
pa ans=mp(inf*2000000000ll*2ll,-1);
while(a<b){
if(a&1){
ans=min(ans,vec[a]);
a++;
}
if(b&1){
b--;
ans=min(ans,vec[b]);
}
a/=2;
b/=2;
}
return ans;
}
};
using fps=vector<long long>;
fps mul(fps x,fps y){
int xl=x.size();
int yl=y.size();
vector<long long> ans(xl+yl-1,0);
for(int i=0;i<xl;i++)for(int j=0;j<yl;j++){
ans[i+j]+=x[i]*y[j]%mod;
if(ans[i+j]>=mod)ans[i+j]-=mod;
}
return ans;
}
vector<long long>first_terms_by_FPS(fps bunsi,fps bunbo){
int a=bunsi.size();
int b=bunbo.size();
assert(a<b);
assert(bunbo[0]!=0);
if(bunbo[0]!=1){
int h=beki(bunbo[0],mod-2);
for(auto &v:bunsi)v=v*h%mod;
for(auto &v:bunbo)v=v*h%mod;
}
while(a!=b-1){
a++;
bunsi.pb(0);
}
for(int i=1;i<a;i++){
for(int j=i-1;j>=0;j--){
bunsi[i]+=mod-bunbo[i-j]*bunsi[j]%mod;
if(bunsi[i]>=mod)bunsi[i]-=mod;
}
}
return bunsi;
}
// A[0],A[1],A[2],..,A[k-1] = first k terms of sequence
// P[0]*A[n] + P[1]*A[n-1] + P[2]*A[n-2] + P[3]*A[n-3] + ... + P[k]A[n-k] = 0
// k>=1
// P[0]!=0 P.back()!=0
// return <bunsi,bunbo>
// O(klogk)
pair<fps,fps> get_fps_form_linear(vector<long long>A,vector<long long>P){
int k=A.size();
int l=P.size();
assert(k+1==l);
fps e=mul(A,P);
for(int i=0;i<k;i++)e.pop_back();
return mp(e,P);
}
int BM2(fps p,fps q,int k){
while(k){
while(q.size()&&q.back()==0)q.pop_back();
while(p.size()&&p.back()==0)p.pop_back();
int pl=p.size();
int ql=q.size();
if(pl==0)return 0;
fps qm=q;
for(int i=1;i<ql;i+=2)if(qm[i])qm[i]=mod-qm[i];
fps e=mul(q,qm);
// s/t
fps s,t;
for(int i=0;i<(int)e.size();i+=2)t.pb(e[i]);
e=mul(p,qm);
if(k%2==0){
for(int i=0;i<(int)e.size();i+=2)s.pb(e[i]);
}
else{
for(int i=1;i<(int)e.size();i+=2)s.pb(e[i]);
}
swap(s,p);
swap(t,q);
k/=2;
}
return p[0]*beki(q[0],mod-2,mod)%mod;
}
int BM(fps p,fps q,int k){
int ps=p.size();
int qs=q.size();
while(k){
while(qs>0&&q.back()==0)q.pop_back(),qs--;
while(ps>0&&p.back()==0)p.pop_back(),ps--;
/*
int pl=p.size();
int ql=q.size();
*/
if(ps==0)return 0;
fps qm=q;
for(int i=1;i<qs;i+=2)if(qm[i])qm[i]=mod-qm[i];
//fps e=mul(q,qm);
int es=qs+qs-1;
// s/t
fps s,t;
t.resize(qs);
for(int i=0;i<qs;i++)for(int j=(i&1);j<qs;j+=2){
t[(i+j)/2]+=q[i]*qm[j]%mod;
if(t[(i+j)/2]>=mod)t[(i+j)/2]-=mod;
}
/*
for(int i=0;i<es;i+=2)t.pb(e[i]);
*/
int ts=(es+1)/2;
//fps e=mul(p,qm);
es=ps+qs-1;
int ss=0;
if(k%2==0){
s.resize((es+1)/2);
for(int i=0;i<ps;i++)for(int j=(i&1);j<qs;j+=2){
s[(i+j)/2]+=p[i]*qm[j]%mod;
if(s[(i+j)/2]>=mod)s[(i+j)/2]-=mod;
}
//for(int i=0;i<es;i+=2)s.pb(e[i]);
ss=(es+1)/2;
}
else{
s.resize(es/2);
for(int i=0;i<ps;i++)for(int j=1-(i&1);j<qs;j+=2){
s[(i+j)/2]+=p[i]*qm[j]%mod;
if(s[(i+j)/2]>=mod)s[(i+j)/2]-=mod;
}
//for(int i=1;i<es;i+=2)s.pb(e[i]);
ss=es/2;
}
ps=ss,qs=ts;
swap(s,p);
swap(t,q);
k/=2;
}
return p[0]*beki(q[0],mod-2,mod)%mod;
}
void solve(){
int p;
cin>>p;
vector<int>ve={0,1};
fps bunbo={1,mod-p,mod-1};
fps bunsi=get_fps_form_linear(ve,bunbo).first;
bunbo=mul(bunbo,bunbo);
bunsi=mul(bunsi,bunsi);
int q;
cin>>q;
while(q--){
int a;
cin>>a;
a-=2;
cout<<BM(bunsi,bunbo,a)<<endl;
}
}
signed main(){
//mod=inf;
cin.tie(0);
ios::sync_with_stdio(false);
int n=1;
//cin>>n;
for(int i=0;i<n;i++)solve();
return 0;
}