結果
| 問題 | No.980 Fibonacci Convolution Hard |
| ユーザー |
👑  tatyam
|
| 提出日時 | 2020-01-31 22:39:52 |
| 言語 | C++17 (gcc 13.2.0 + boost 1.83.0) |
| 結果 |
AC
|
| 実行時間 | 1,126 ms / 2,000 ms |
| コード長 | 17,175 bytes |
| コンパイル時間 | 3,429 ms |
| コンパイル使用メモリ | 236,376 KB |
| 実行使用メモリ | 76,008 KB |
| 最終ジャッジ日時 | 2023-10-17 13:46:30 |
| 合計ジャッジ時間 | 25,751 ms |
|
ジャッジサーバーID （参考情報） |
judge11 / judge15 |
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 | 1,106 ms
76,008 KB |
| testcase_01 | AC | 1,106 ms
76,008 KB |
| testcase_02 | AC | 1,114 ms
76,008 KB |
| testcase_03 | AC | 1,116 ms
76,008 KB |
| testcase_04 | AC | 1,107 ms
76,008 KB |
| testcase_05 | AC | 1,126 ms
76,008 KB |
| testcase_06 | AC | 1,108 ms
76,008 KB |
| testcase_07 | AC | 1,118 ms
76,008 KB |
| testcase_08 | AC | 1,108 ms
76,008 KB |
| testcase_09 | AC | 1,108 ms
76,008 KB |
| testcase_10 | AC | 1,110 ms
76,008 KB |
| testcase_11 | AC | 1,117 ms
76,008 KB |
| testcase_12 | AC | 1,107 ms
76,008 KB |
| testcase_13 | AC | 1,113 ms
76,008 KB |
| testcase_14 | AC | 1,117 ms
76,008 KB |
| testcase_15 | AC | 1,124 ms
76,008 KB |
| testcase_16 | AC | 1,092 ms
76,008 KB |
ソースコード
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ld = long double;
using ull = unsigned long long;
using uint = unsigned int;
using pcc = pair<char, char>;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
using pdd = pair<double, double>;
using tuplis = array<ll, 3>;
template<class T> using pq = priority_queue<T, vector<T>, greater<T>>;
const ll LINF=0x1fffffffffffffff;
const ll MINF=0x7fffffffffff;
const int INF=0x3fffffff;
const int MOD=1000000007;
const int MODD=998244353;
const ld DINF=numeric_limits<ld>::infinity();
const ld EPS=1e-9;
const ld PI=3.1415926535897932;
const ll four[] = {0, 1, 0, -1, 0};
const ll eight[] = {0, 1, 1, 0, -1, -1, 1, -1, 0};
#define overload4(_1,_2,_3,_4,name,...) name
#define overload3(_1,_2,_3,name,...) name
#define rep1(n) for(ll i=0;i<n;++i)
#define rep2(i,n) for(ll i=0;i<n;++i)
#define rep3(i,a,b) for(ll i=a;i<b;++i)
#define rep4(i,a,b,c) for(ll i=a;i<b;i+=c)
#define rep(...) overload4(__VA_ARGS__,rep4,rep3,rep2,rep1)(__VA_ARGS__)
#define rrep1(n) for(ll i=(n)-1;i>=0;i--)
#define rrep2(i,n) for(ll i=(n)-1;i>=0;i--)
#define rrep3(i,a,b) for(ll i=(b)-1;i>=(a);i--)
#define rrep4(i,a,b,c) for(ll i=a+(b-a-1)/c*c;i>=a;i-=c)
#define rrep(...) overload4(__VA_ARGS__,rrep4,rrep3,rrep2,rrep1)(__VA_ARGS__)
#define each(i,...) for(auto&& i:__VA_ARGS__)
#define all1(i) begin(i),end(i)
#define all2(i,a) begin(i),begin(i)+a
#define all3(i,a,b) begin(i)+a,begin(i)+b
#define all(...) overload3(__VA_ARGS__,all3,all2,all1)(__VA_ARGS__)
#define rall1(i) (i).rbegin(),(i).rend()
#define rall2(i,k) (i).rbegin(),(i).rbegin()+k
#define rall3(i,a,b) (i).rbegin()+a,(i).rbegin()+b
#define rall(...) overload3(__VA_ARGS__,rall3,rall2,rall1)(__VA_ARGS__)
#define sum(...) accumulate(all(__VA_ARGS__),0LL)
#define dsum(...) accumulate(all(__VA_ARGS__),0.0L)
#define elif else if
#define unless(a) if(!(a))
#define mp make_pair
#define mt make_tuple
#define INT(...) int __VA_ARGS__;in(__VA_ARGS__)
#define LL(...) ll __VA_ARGS__;in(__VA_ARGS__)
#define ULL(...) ull __VA_ARGS__;in(__VA_ARGS__)
#define STR(...) string __VA_ARGS__;in(__VA_ARGS__)
#define CHR(...) char __VA_ARGS__;in(__VA_ARGS__)
#define DBL(...) double __VA_ARGS__;in(__VA_ARGS__)
#define LD(...) ld __VA_ARGS__;in(__VA_ARGS__)
#define vec(type,name,...) vector<type> name(__VA_ARGS__)
#define VEC(type,name,size) vector<type> name(size);in(name)
#define vv(type,name,h,...) vector<vector<type>>name(h,vector<type>(__VA_ARGS__))
#define VV(type,name,h,w) vector<vector<type>>name(h,vector<type>(w));in(name)
#define vvv(type,name,h,w,...) vector<vector<vector<type>>>name(h,vector<vector<type>>(w,vector<type>(__VA_ARGS__)))
template<class T> auto max(const T& a){ return *max_element(all(a)); }
template<class T> auto min(const T& a){ return *min_element(all(a)); }
ll gcd(ll a, ll b){ while(b){ ll c = b; b = a % b; a = c; } return a; }
ll lcm(ll a, ll b){ if(!a || !b) return 0; return a * b / gcd(a, b); }
ll intpow(ll a, ll b){ ll ans = 1; while(b){ if(b & 1) ans *= a; a *= a; b /= 2; } return ans; }
ll modpow(ll a, ll b, ll p){ ll ans = 1; while(b){ if(b & 1) (ans *= a) %= p; (a *= a) %= p; b /= 2; } return ans; }
template<class T> bool chmin(T& a, const T& b){ if(a > b){ a = b; return 1; } return 0; }
template<class T> bool chmax(T& a, const T& b){ if(a < b){ a = b; return 1; } return 0; }
vector<pll> factor(ull x){ vector<pll> ans; for(ll i = 2; i * i <= x; i++) if(x % i == 0){ ans.push_back({i, 1}); while((x /= i) % i == 0) ans.back().second++; } if(x != 1) ans.push_back({x, 1}); return ans; }
vector<ll> divisor(ull x){ vector<ll> ans; for(ll i = 1; i * i <= x; i++) if(x % i == 0) ans.push_back(i); rrep(ans.size() - (ans.back() * ans.back() == x)) ans.push_back(x / ans[i]); return ans; }
template<class T> unordered_map<T, ll> press(vector<T>& a){ auto b = a; sort(all(b)); b.erase(unique(all(b)), b.end()); unordered_map<T,ll> ans; rep(b.size()) ans[b[i]] = i; each(i, a) i = ans[i]; return ans; }
template<class T> map<T, ll> press_map(vector<T>& a){ auto b = a; sort(all(b)); b.erase(unique(all(b)), b.end()); map<T,ll> ans; rep(b.size()) ans[b[i]] = i; each(i, a) i = ans[i]; return ans; }
int scan(){ return getchar(); }
void scan(int& a){ scanf("%d", &a); }
void scan(unsigned& a){ scanf("%u", &a); }
void scan(long& a){ scanf("%ld", &a); }
void scan(long long& a){ scanf("%lld", &a); }
void scan(unsigned long long& a){ scanf("%llu", &a); }
void scan(char& a){ do{ a = getchar(); }while(a == ' ' || a == '\n'); }
void scan(float& a){ scanf("%f", &a); }
void scan(double& a){ scanf("%lf", &a); }
void scan(long double& a){ scanf("%Lf", &a); }
void scan(vector<bool>& a){ for(unsigned i = 0; i < a.size(); i++) { int b; scan(b); a[i] = b; } }
void scan(char a[]){ scanf("%s", a); }
void scan(string& a){ cin >> a; }
template<class T> void scan(vector<T>&);
template<class T, size_t size> void scan(array<T, size>&);
template<class T, class L> void scan(pair<T, L>&);
template<class T, size_t size> void scan(T(&)[size]);
template<class T> void scan(vector<T>& a){ for(auto&& i : a) scan(i); }
template<class T> void scan(deque<T>& a){ for(auto&& i : a) scan(i); }
template<class T, size_t size> void scan(array<T, size>& a){ for(auto&& i : a) scan(i); }
template<class T, class L> void scan(pair<T, L>& p){ scan(p.first); scan(p.second); }
template<class T, size_t size> void scan(T (&a)[size]){ for(auto&& i : a) scan(i); }
template<class T> void scan(T& a){ cin >> a; }
void in(){}
template <class Head, class... Tail> void in(Head& head, Tail&... tail){ scan(head); in(tail...); }
void print(){ putchar(' '); }
void print(bool a){ printf("%d", a); }
void print(int a){ printf("%d", a); }
void print(unsigned a){ printf("%u", a); }
void print(long a){ printf("%ld", a); }
void print(long long a){ printf("%lld", a); }
void print(unsigned long long a){ printf("%llu", a); }
void print(char a){ printf("%c", a); }
void print(char a[]){ printf("%s", a); }
void print(const char a[]){ printf("%s", a); }
void print(float a){ printf("%.15f", a); }
void print(double a){ printf("%.15f", a); }
void print(long double a){ printf("%.15Lf", a); }
void print(const string& a){ for(auto&& i : a) print(i); }
template<class T> void print(const vector<T>&);
template<class T, size_t size> void print(const array<T, size>&);
template<class T, class L> void print(const pair<T, L>& p);
template<class T, size_t size> void print(const T (&)[size]);
template<class T> void print(const vector<T>& a){ if(a.empty()) return; print(a[0]); for(auto i = a.begin(); ++i != a.end(); ){ putchar(' '); print(*i); } }
template<class T> void print(const deque<T>& a){ if(a.empty()) return; print(a[0]); for(auto i = a.begin(); ++i != a.end(); ){ putchar(' '); print(*i); } }
template<class T, size_t size> void print(const array<T, size>& a){ print(a[0]); for(auto i = a.begin(); ++i != a.end(); ){ putchar(' '); print(*i); } }
template<class T, class L> void print(const pair<T, L>& p){ print(p.first); putchar(' '); print(p.second); }
template<class T, size_t size> void print(const T (&a)[size]){ print(a[0]); for(auto i = a; ++i != end(a); ){ putchar(' '); print(*i); } }
template<class T> void print(const T& a){ cout << a; }
int out(){ putchar('\n'); return 0; }
template<class T> int out(const T& t){ print(t); putchar('\n'); return 0; }
template<class Head, class... Tail> int out(const Head& head, const Tail&... tail){ print(head); putchar(' '); out(tail...); return 0; }
#ifdef DEBUG
void err(){ putchar('\n'); }
template<class T> void err(const T& t){ print(t); putchar('\n'); }
template<class Head, class... Tail> void err(const Head& head, const Tail&... tail){ print(head); putchar(' '); out(tail...); }
#else
template<class... T> void err(const T&...){}
#endif
int first(bool i = true){ return out(i?"first":"second"); }
int yes(bool i = true){ return out(i?"yes":"no"); }
int Yes(bool i = true){ return out(i?"Yes":"No"); }
int No(){ return out("No"); }
int YES(bool i = true){ return out(i?"YES":"NO"); }
int NO(){ return out("NO"); }
int Yay(bool i = true){ return out(i?"Yay!":":("); }
int possible(bool i = true){ return out(i?"possible":"impossible"); }
int Possible(bool i = true){ return out(i?"Possible":"Impossible"); }
int POSSIBLE(bool i = true){ return out(i?"POSSIBLE":"IMPOSSIBLE"); }
void Case(ll i){ printf("Case #%lld: ", i); }
using uint=unsigned;
using ull=unsigned long long;
template<class t> using vc=vector<t>;
#define rng(i,a,b) for(int i=int(a);i<int(b);i++)
#define si(x) int(x.size())
#define pb push_back
#ifdef DEBUG
inline constexpr int __lg(int __n) { return sizeof(int) * __CHAR_BIT__ - 1 - __builtin_clz(__n); }
#endif
struct modinfo{uint mod,root;};
template<modinfo const&ref>
struct modular{
static constexpr uint const &mod=ref.mod;
static modular root(){return modular(ref.root);}
uint v;
//modular(initializer_list<uint>ls):v(*ls.bg){}
modular(ll vv=0){s(vv%mod+mod);}
modular& s(uint vv){
v=vv<mod?vv:vv-mod;
return *this;
}
modular operator-()const{return modular()-*this;}
modular& operator+=(const modular&rhs){return s(v+rhs.v);}
modular&operator-=(const modular&rhs){return s(v+mod-rhs.v);}
modular&operator*=(const modular&rhs){
v=ull(v)*rhs.v%mod;
return *this;
}
modular&operator/=(const modular&rhs){return *this*=rhs.inv();}
modular operator+(const modular&rhs)const{return modular(*this)+=rhs;}
modular operator-(const modular&rhs)const{return modular(*this)-=rhs;}
modular operator*(const modular&rhs)const{return modular(*this)*=rhs;}
modular operator/(const modular&rhs)const{return modular(*this)/=rhs;}
modular pow(int n)const{
modular res(1),x(*this);
while(n){
if(n&1)res*=x;
x*=x;
n>>=1;
}
return res;
}
modular inv()const{return pow(mod-2);}
/*modular inv()const{
int x,y;
int g=extgcd(v,mod,x,y);
assert(g==1);
if(x<0)x+=mod;
return modular(x);
}*/
friend modular operator+(int x,const modular&y){
return modular(x)+y;
}
friend modular operator-(int x,const modular&y){
return modular(x)-y;
}
friend modular operator*(int x,const modular&y){
return modular(x)*y;
}
friend modular operator/(int x,const modular&y){
return modular(x)/y;
}
friend ostream& operator<<(ostream&os,const modular&m){
return os<<m.v;
}
friend istream& operator>>(istream&is,modular&m){
ll x;is>>x;
m=modular(x);
return is;
}
bool operator<(const modular&r)const{return v<r.v;}
bool operator==(const modular&r)const{return v==r.v;}
bool operator!=(const modular&r)const{return v!=r.v;}
explicit operator bool()const{
return v;
}
};
#define USE_FMT
/*
//998244353
const mint prim_root=3;
//in-place fft
//size of input must be a power of 2
void inplace_fmt(vector<mint>&f,const bool inv){
const int n=f.size();
const mint root=inv?prim_root.inv():prim_root;
vc<mint> g(n);
for(int b=n/2;b>=1;b/=2){
mint w=root.pow((mint::base-1)/(n/b)),p=1;
for(int i=0;i<n;i+=b*2){
rep(j,b){
f[i+j+b]*=p;
g[i/2+j]=f[i+j]+f[i+b+j];
g[n/2+i/2+j]=f[i+j]-f[i+b+j];
}
p*=w;
}
swap(f,g);
}
if(inv)rep(i,n)
f[i]*=inv[n];
}*/
//size of input must be a power of 2
//output of forward fmt is bit-reversed
//output elements are in the range [0,mod*4)
//input of inverse fmt should be bit-reversed
template<class mint>
void inplace_fmt(vector<mint>&f,bool inv){
const int n=si(f);
static vc<mint> g,ig,p2;
if(si(g)==0){
rep(i,30){
mint w=-mint::root().pow(((mint::mod-1)>>(i+2))*3);
g.pb(w);
ig.pb(w.inv());
p2.pb(mint(1<<i).inv());
}
}
static constexpr uint mod2=mint::mod*2;
if(!inv){
int b=n;
if(b>>=1){//input:[0,mod)
rep(i,b){
uint x=f[i+b].v;
f[i+b].v=f[i].v+mint::mod-x;
f[i].v+=x;
}
}
if(b>>=1){//input:[0,mod*2)
mint p=1;
for(int i=0,k=0;i<n;i+=b*2){
rng(j,i,i+b){
uint x=(f[j+b]*p).v;
//f[j].v=(f[j].v<mint::mod?f[j].v:f[j].v-mint::mod);
f[j+b].v=f[j].v+mint::mod-x;
f[j].v+=x;
}
p*=g[__builtin_ctz(++k)];
}
}
while(b){
if(b>>=1){//input:[0,mod*3)
mint p=1;
for(int i=0,k=0;i<n;i+=b*2){
rng(j,i,i+b){
uint x=(f[j+b]*p).v;
//f[j].v=(f[j].v<mint::mod?f[j].v:f[j].v-mint::mod);
f[j+b].v=f[j].v+mint::mod-x;
f[j].v+=x;
}
p*=g[__builtin_ctz(++k)];
}
}
if(b>>=1){//input:[0,mod*4)
mint p=1;
for(int i=0,k=0;i<n;i+=b*2){
rng(j,i,i+b){
uint x=(f[j+b]*p).v;
f[j].v=(f[j].v<mod2?f[j].v:f[j].v-mod2);
f[j+b].v=f[j].v+mint::mod-x;
f[j].v+=x;
}
p*=g[__builtin_ctz(++k)];
}
}
}
}else{
int b=1;
if(b<n/2){//input:[0,mod)
mint p=1;
for(int i=0,k=0;i<n;i+=b*2){
rng(j,i,i+b){
ull x=f[j].v+mint::mod-f[j+b].v;
f[j].v+=f[j+b].v;
f[j+b].v=x*p.v%mint::mod;
}
p*=ig[__builtin_ctz(++k)];
}
b<<=1;
}
for(;b<n/2;b<<=1){
mint p=1;
for(int i=0,k=0;i<n;i+=b*2){
rng(j,i,i+b/2){//input:[0,mod*2)
ull x=f[j].v+mod2-f[j+b].v;
f[j].v+=f[j+b].v;
f[j].v=(f[j].v)<mod2?f[j].v:f[j].v-mod2;
f[j+b].v=x*p.v%mint::mod;
}
rng(j,i+b/2,i+b){//input:[0,mod)
ull x=f[j].v+mint::mod-f[j+b].v;
f[j].v+=f[j+b].v;
//f[j].v=(f[j].v)<mod2?f[j].v:f[j].v-mod2;
f[j+b].v=x*p.v%mint::mod;
}
p*=ig[__builtin_ctz(++k)];
}
}
if(b<n){//input:[0,mod*2)
rep(i,b){
uint x=f[i+b].v;
f[i+b].v=f[i].v+mod2-x;
f[i].v+=x;
}
}
mint z=p2[__lg(n)];
rep(i,n)f[i]*=z;
}
}
/*
template<class mint>
vc<mint> multiply(vc<mint> x,const vc<mint>&y,bool same=false){
int n=si(x)+si(y)-1;
int s=1;
while(s<n)s*=2;
x.resize(s);inplace_fmt(x,false);
if(!same){
vc<mint> z(s);
rep(i,si(y))z[i]=y[i];
inplace_fmt(z,false);
rep(i,s)x[i]*=z[i];
}else{
rep(i,s)x[i]*=x[i];
}
inplace_fmt(x,true);x.resize(n);
return x;
}
*/
//59501818244292734739283969=5.95*10^25 までの値を正しく計算
//最終的な列の大きさが 2^24 までなら動く
namespace arbitrary_convolution{
constexpr modinfo base0{167772161,3};//2^25 * 5 + 1
constexpr modinfo base1{469762049,3};//2^26 * 7 + 1
constexpr modinfo base2{754974721,11};//2^24 * 45 + 1
using mint0=modular<base0>;
using mint1=modular<base1>;
using mint2=modular<base2>;
template<class t,class mint>
vc<t> sub(const vc<mint>&x,const vc<mint>&y,bool same=false){
int n=si(x)+si(y)-1;
int s=1;
while(s<n)s*=2;
vc<t> z(s);rep(i,si(x))z[i]=x[i].v;
inplace_fmt(z,false);
if(!same){
vc<t> w(s);rep(i,si(y))w[i]=y[i].v;
inplace_fmt(w,false);
rep(i,s)z[i]*=w[i];
}else{
rep(i,s)z[i]*=z[i];
}
inplace_fmt(z,true);z.resize(n);
return z;
}
template<class mint>
vc<mint> multiply(const vc<mint>&x,const vc<mint>&y,bool same=false){
auto d0=sub<mint0>(x,y,same);
auto d1=sub<mint1>(x,y,same);
auto d2=sub<mint2>(x,y,same);
int n=si(d0);
vc<mint> res(n);
static mint1 r01=mint1(mint0::mod).inv();
static mint2 r02=mint2(mint0::mod).inv();
static mint2 r12=mint2(mint1::mod).inv();
static mint w1=mint(mint0::mod);
static mint w2=w1*mint(mint1::mod);
rep(i,n){
{
uint z=d0[i].v;
res[i]+=z;
d1[i]=(d1[i]-z)*r01;
d2[i]=(d2[i]-z)*r02;
}
{
uint z=d1[i].v;
res[i]+=w1*z;
d2[i]=(d2[i]-z)*r12;
}
{
uint z=d2[i].v;
res[i]+=w2*z;
}
}
return res;
}
}
using arbitrary_convolution::multiply;
constexpr modinfo base{1000000007,0};
using mint=modular<base>;
signed main(){
LL(p,q);
vec(mint,a,2000001);
a[2]=1;
rep(i,3,2000001)a[i]=a[i-1]*p+a[i-2];
auto c=multiply(a,a,true);
rep(q){
LL(a);
out(c[a]);
}
}