結果

問題 No.980 Fibonacci Convolution Hard
ユーザー snukesnuke
提出日時 2020-01-31 21:49:15
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 417 ms / 2,000 ms
コード長 8,071 bytes
コンパイル時間 2,906 ms
コンパイル使用メモリ 219,212 KB
実行使用メモリ 34,560 KB
最終ジャッジ日時 2024-09-17 11:26:24
合計ジャッジ時間 12,425 ms
ジャッジサーバーID
（参考情報） 		judge1 / judge2
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 409 ms
34,432 KB
testcase_01 AC 410 ms
34,560 KB
testcase_02 AC 403 ms
34,560 KB
testcase_03 AC 411 ms
34,432 KB
testcase_04 AC 404 ms
34,492 KB
testcase_05 AC 410 ms
34,432 KB
testcase_06 AC 399 ms
34,432 KB
testcase_07 AC 400 ms
34,432 KB
testcase_08 AC 411 ms
34,444 KB
testcase_09 AC 413 ms
34,560 KB
testcase_10 AC 408 ms
34,560 KB
testcase_11 AC 401 ms
34,560 KB
testcase_12 AC 417 ms
34,432 KB
testcase_13 AC 403 ms
34,560 KB
testcase_14 AC 412 ms
34,428 KB
testcase_15 AC 410 ms
34,304 KB
testcase_16 AC 375 ms
34,432 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>
#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;
}
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