結果

問題 No.980 Fibonacci Convolution Hard
ユーザー tatyamtatyam
提出日時 2020-01-31 22:39:52
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 1,019 ms / 2,000 ms
コード長 17,175 bytes
コンパイル時間 2,987 ms
コンパイル使用メモリ 236,836 KB
実行使用メモリ 75,984 KB
最終ジャッジ日時 2024-09-17 11:38:51
合計ジャッジ時間 23,365 ms
ジャッジサーバーID
（参考情報） 		judge6 / judge5
このコードへのチャレンジ
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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 972 ms
75,920 KB
testcase_01 AC 995 ms
75,916 KB
testcase_02 AC 999 ms
75,792 KB
testcase_03 AC 999 ms
75,760 KB
testcase_04 AC 985 ms
75,904 KB
testcase_05 AC 1,019 ms
75,920 KB
testcase_06 AC 1,007 ms
75,852 KB
testcase_07 AC 1,016 ms
75,936 KB
testcase_08 AC 996 ms
75,984 KB
testcase_09 AC 1,009 ms
75,968 KB
testcase_10 AC 1,009 ms
75,928 KB
testcase_11 AC 1,011 ms
75,760 KB
testcase_12 AC 1,006 ms
75,780 KB
testcase_13 AC 1,019 ms
75,944 KB
testcase_14 AC 1,007 ms
75,904 KB
testcase_15 AC 1,012 ms
75,904 KB
testcase_16 AC 992 ms
75,896 KB
権限があれば一括ダウンロードができます

ソースコード

diff # 

#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]);
    }
}
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