結果
| 問題 |
No.980 Fibonacci Convolution Hard
|
| ユーザー |
 snuke
|
| 提出日時 | 2020-01-31 21:49:15 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 382 ms / 2,000 ms |
| コード長 | 8,071 bytes |
| コンパイル時間 | 2,558 ms |
| コンパイル使用メモリ | 211,544 KB |
| 最終ジャッジ日時 | 2025-01-08 21:01:02 |
|
ジャッジサーバーID （参考情報） |
judge1 / judge2 |
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| ファイルパターン | 結果 |
|---|---|
| other | AC * 17 |
ソースコード
#include <bits/stdc++.h>
#define fi first
#define se second
#define rep(i,n) for(int i = 0; i < (n); ++i)
#define rrep(i,n) for(int i = 1; i <= (n); ++i)
#define drep(i,n) for(int i = (n)-1; i >= 0; --i)
#define srep(i,s,t) for (int i = s; i < t; ++i)
#define rng(a) a.begin(),a.end()
#define rrng(a) a.rbegin(),a.rend()
#define maxs(x,y) (x = max(x,y))
#define mins(x,y) (x = min(x,y))
#define limit(x,l,r) max(l,min(x,r))
#define lims(x,l,r) (x = max(l,min(x,r)))
#define isin(x,l,r) ((l) <= (x) && (x) < (r))
#define pb push_back
#define eb emplace_back
#define sz(x) (int)(x).size()
#define pcnt __builtin_popcountll
#define uni(x) x.erase(unique(rng(x)),x.end())
#define snuke srand((unsigned)clock()+(unsigned)time(NULL));
#define show(x) cout<<#x<<" = "<<x<<endl;
#define PQ(T) priority_queue<T,v(T),greater<T> >
#define bn(x) ((1<<x)-1)
#define dup(x,y) (((x)+(y)-1)/(y))
#define newline puts("")
#define v(T) vector<T>
#define vv(T) v(v(T))
using namespace std;
typedef long long int ll;
typedef unsigned uint;
typedef unsigned long long ull;
typedef pair<int,int> P;
typedef tuple<int,int,int> T;
typedef vector<int> vi;
typedef vector<vi> vvi;
typedef vector<ll> vl;
typedef vector<P> vp;
typedef vector<T> vt;
inline int in() { int x; scanf("%d",&x); return x;}
template<typename T>inline istream& operator>>(istream&i,v(T)&v)
{rep(j,sz(v))i>>v[j];return i;}
template<typename T>string join(const v(T)&v)
{stringstream s;rep(i,sz(v))s<<' '<<v[i];return s.str().substr(1);}
template<typename T>inline ostream& operator<<(ostream&o,const v(T)&v)
{if(sz(v))o<<join(v);return o;}
template<typename T1,typename T2>inline istream& operator>>(istream&i,pair<T1,T2>&v)
{return i>>v.fi>>v.se;}
template<typename T1,typename T2>inline ostream& operator<<(ostream&o,const pair<T1,T2>&v)
{return o<<v.fi<<","<<v.se;}
template<typename T>inline ll suma(const v(T)& a) { ll res(0); for (auto&& x : a) res += x; return res;}
const double eps = 1e-10;
const ll LINF = 1001002003004005006ll;
const int INF = 1001001001;
#define dame { puts("-1"); return 0;}
#define yn {puts("Yes");}else{puts("No");}
const int MX = 200005;
// Mod int
const int mod = 1000000007;
// const int mod = 998244353;
struct mint {
ll x;
mint():x(0){}
mint(ll x):x((x%mod+mod)%mod){}
// mint(ll x):x(x){}
mint& fix() { x = (x%mod+mod)%mod; return *this;}
mint operator-() const { return mint(0) - *this;}
mint operator~() const { return mint(1) / *this;}
mint& operator+=(const mint& a){ if((x+=a.x)>=mod) x-=mod; return *this;}
mint& operator-=(const mint& a){ if((x+=mod-a.x)>=mod) x-=mod; return *this;}
mint& operator*=(const mint& a){ (x*=a.x)%=mod; return *this;}
mint& operator/=(const mint& a){ (x*=a.pow(mod-2).x)%=mod; return *this;}
mint operator+(const mint& a)const{ return mint(*this) += a;}
mint operator-(const mint& a)const{ return mint(*this) -= a;}
mint operator*(const mint& a)const{ return mint(*this) *= a;}
mint operator/(const mint& a)const{ return mint(*this) /= a;}
mint pow(ll t) const {
if(!t) return 1;
mint res = pow(t/2);
res *= res;
return (t&1)?res*x:res;
}
bool operator<(const mint& a)const{ return x < a.x;}
bool operator==(const mint& a)const{ return x == a.x;}
};
mint ex(mint x, ll t) { return x.pow(t);}
istream& operator>>(istream&i,mint&a){i>>a.x;return i;}
ostream& operator<<(ostream&o,const mint&a){o<<a.x;return o;}
typedef vector<mint> vm;
struct comb {
vm f, g;
comb(){}
comb(int mx):f(mx+1),g(mx+1) {
f[0] = 1;
rrep(i,mx) f[i] = f[i-1]*i;
g[mx] = f[mx].pow(mod-2);
for(int i=mx;i>0;i--) g[i-1] = g[i]*i;
}
mint c(int a, int b) {
if (a < b) return 0;
return f[a]*g[b]*g[a-b];
}
};
//
// NTT
template<class T> T extgcd(T a, T b, T& x, T& y) { for (T u = y = 1, v = x = 0; a;) { T q = b / a; swap(x -= q * u, u); swap(y -= q * v, v); swap(b -= q * a, a); } return b; }
template<class T> T mod_inv(T a, T m) { T x, y; extgcd(a, m, x, y); return (m + x % m) % m; }
ll mod_pow(ll a, ll n, ll mod) { ll ret = 1; ll p = a % mod; while (n) { if (n & 1) ret = ret * p % mod; p = p * p % mod; n >>= 1; } return ret; }
template<int mod, int primitive_root>
class NTT {
public:
int get_mod() const { return mod; }
void _ntt(vl& a, int sign) {
const int n = sz(a);
const int g = primitive_root; //g is primitive root of mod
int h = (int)mod_pow(g, (mod - 1) / n, mod); // h^n = 1
if (sign == -1) h = (int)mod_inv(h, mod); //h = h^-1 % mod
int i = 0;
for (int j = 1; j < n - 1; ++j) {
for (int k = n >> 1; k >(i ^= k); k >>= 1);
if (j < i) swap(a[i], a[j]);
}
for (int m = 1; m < n; m *= 2) {
const int m2 = 2 * m;
const ll base = mod_pow(h, n / m2, mod);
ll w = 1;
rep(x, m) {
for (int s = x; s < n; s += m2) {
ll u = a[s];
ll d = a[s + m] * w % mod;
a[s] = u + d;
if (a[s] >= mod) a[s] -= mod;
a[s + m] = u - d;
if (a[s + m] < 0) a[s + m] += mod;
}
w = w * base % mod;
}
}
for (auto& x : a) if (x < 0) x += mod;
}
void ntt(vl& input) {
_ntt(input, 1);
}
void intt(vl& input) {
_ntt(input, -1);
const int n_inv = mod_inv(sz(input), mod);
for (auto& x : input) x = x * n_inv % mod;
}
vl convolution(const vl& a, const vl& b){
int ntt_size = 1;
while (ntt_size < sz(a) + sz(b)) ntt_size *= 2;
vl _a = a, _b = b;
_a.resize(ntt_size); _b.resize(ntt_size);
ntt(_a);
ntt(_b);
rep(i, ntt_size){
(_a[i] *= _b[i]) %= mod;
}
intt(_a);
return _a;
}
};
ll garner(vp mr, int mod){
mr.emplace_back(mod, 0);
vl coffs(sz(mr), 1);
vl constants(sz(mr), 0);
rep(i, sz(mr) - 1){
// coffs[i] * v + constants[i] == mr[i].second (mod mr[i].first)
ll v = (mr[i].second - constants[i]) * mod_inv<ll>(coffs[i], mr[i].first) % mr[i].first;
if (v < 0) v += mr[i].first;
for (int j = i + 1; j < sz(mr); j++) {
(constants[j] += coffs[j] * v) %= mr[j].first;
(coffs[j] *= mr[i].first) %= mr[j].first;
}
}
return constants[sz(mr) - 1];
}
typedef NTT<167772161, 3> NTT_1;
typedef NTT<469762049, 3> NTT_2;
typedef NTT<1224736769, 3> NTT_3;
vl int32mod_convolution(vl a, vl b,int mod){
for (auto& x : a) x %= mod;
for (auto& x : b) x %= mod;
NTT_1 ntt1; NTT_2 ntt2; NTT_3 ntt3;
auto x = ntt1.convolution(a, b);
auto y = ntt2.convolution(a, b);
auto z = ntt3.convolution(a, b);
vl ret(sz(x));
vp mr(3);
rep(i, sz(x)){
mr[0].first = ntt1.get_mod(), mr[0].second = (int)x[i];
mr[1].first = ntt2.get_mod(), mr[1].second = (int)y[i];
mr[2].first = ntt3.get_mod(), mr[2].second = (int)z[i];
ret[i] = garner(mr, mod);
}
return ret;
}
vl fast_int32mod_convolution(vl a, vl b,int mod){
for (auto& x : a) x %= mod;
for (auto& x : b) x %= mod;
NTT_1 ntt1; NTT_2 ntt2; NTT_3 ntt3;
auto x = ntt1.convolution(a, b);
auto y = ntt2.convolution(a, b);
auto z = ntt3.convolution(a, b);
const ll m1 = ntt1.get_mod(), m2 = ntt2.get_mod(), m3 = ntt3.get_mod();
const ll m1_inv_m2 = mod_inv<ll>(m1, m2);
const ll m12_inv_m3 = mod_inv<ll>(m1 * m2, m3);
const ll m12_mod = m1 * m2 % mod;
vl ret(sz(x));
rep(i, sz(x)){
ll v1 = (y[i] - x[i]) * m1_inv_m2 % m2;
if (v1 < 0) v1 += m2;
ll v2 = (z[i] - (x[i] + m1 * v1) % m3) * m12_inv_m3 % m3;
if (v2 < 0) v2 += m3;
ll constants3 = (x[i] + m1 * v1 + m12_mod * v2) % mod;
if (constants3 < 0) constants3 += mod;
ret[i] = constants3;
}
return ret;
}
//
int main() {
int n, p;
n = 2000000;
cin>>p;
int q;
cin>>q;
vm a(n);
a[0] = 0;
a[1] = 1;
rep(i,n) {
if (i < 2) continue;
a[i] = a[i-1]*p+a[i-2];
}
// vl x(n);
// rep(i,n) x[i] = a[i].x;
// vl d = fast_int32mod_convolution(x,x,mod);
vm d(n);
rep(i,5) {
rep(j,i+1) d[i] += a[j]*a[i-j];
}
srep(i,5,n) {
d[i] = d[i-1]*p;
d[i] += d[i-2];
d[i] += a[i-1]*a[1];
}
rep(qi,q) {
int s;
cin>>s;
s -= 2;
cout<<d[s]<<endl;
}
return 0;
}