#713832 (C++17) No.42 貯金箱の溜息

• 問題: No.42 貯金箱の溜息
• ユーザー: PCTprobability
• 提出日時: 2021-11-06 18:26:44
• 言語: C++17 (gcc 12.3.0 + boost 1.83.0)
• 結果: TLE
• 実行時間: -
• コード長: 15,744 bytes
• コンパイル時間: 5,683 ms
• コンパイル使用メモリ: 282,664 KB
• 実行使用メモリ: 8,832 KB
• 最終ジャッジ日時: 2024-11-07 17:12:30
• 合計ジャッジ時間: 18,452 ms
• ジャッジサーバーID （参考情報）: judge5 / judge1

入力	結果	実行時間; 実行使用メモリ
testcase_00	TLE	-
testcase_01	--	-
testcase_02	--	-

ソースコード

#include <bits/stdc++.h>
using namespace std;
#if __has_include(<atcoder/all>)
#include <atcoder/all>
using namespace atcoder;
#endif
using ll = long long;
using ld = long double;
using ull = unsigned long long;
#define endl "\n"
typedef pair<int, int> Pii;
#define REP(i, n) for (int i = 0; i < (n); ++i)
#define REP3(i, m, n) for (int i = (m); (i) < int(n); ++ (i))
#define FOR(i,a,b) for(ll i=a;i<=(ll)(b);i++)
#define rep(i,a,b) for(int i=(int)(a);i<(int)(b);i++)
#define ALL(x) begin(x), end(x)
#define PB push_back
#define rrep(i,a,b) for(int i=a;i>=b;i--)
#define fore(i,a) for(auto &i:a)
#define all(s) (s).begin(),(s).end()
#define drep2(i, m, n) for (int i = (m)-1; i >= (n); --i)
#define drep(i, n) drep2(i, n, 0)
#define rever(vec) reverse(vec.begin(), vec.end())
#define sor(vec) sort(vec.begin(), vec.end())
#define fi first
#define se second
#define pb push_back
#define P pair<ll,ll>
#define PQminll priority_queue<ll, vector<ll>, greater<ll>>
#define PQmaxll priority_queue<ll,vector<ll>,less<ll>>
#define PQminP priority_queue<P, vector<P>, greater<P>>
#define PQmaxP priority_queue<P,vector<P>,less<P>>
#define NP next_permutation
typedef string::const_iterator State;
class ParseError {};
//const ll mod = 1000000009;
const ll mod = 998244353;
//const ll mod = 1000000007;
const ll inf = 4100000000000000000ll;
const ld eps = ld(0.00000000000001);
//static const long double pi = 3.141592653589793;
template<class T>void vcin(vector<T> &n){for(int i=0;i<int(n.size());i++) cin>>n[i];}
template<class T,class K>void vcin(vector<T> &n,vector<K> &m){for(int i=0;i<int(n.size());i++) cin>>n[i]>>m[i];}
template<class T>void vcout(vector<T> &n){for(int i=0;i<int(n.size());i++){cout<<n[i]<<" ";}cout<<endl;}
template<class T>void vcin(vector<vector<T>> &n){for(int i=0;i<int(n.size());i++){for(int j=0;j<int(n[i].size());j++){cin>>n[i][j];}}}
template<class T>void vcout(vector<vector<T>> &n){for(int i=0;i<int(n.size());i++){for(int j=0;j<int(n[i].size());j++){cout<<n[i][j]<<" ";}cout<<endl;}cout<<endl;}
void yes(bool a){cout<<(a?"yes":"no")<<endl;}
void YES(bool a){cout<<(a?"YES":"NO")<<endl;}
void Yes(bool a){cout<<(a?"Yes":"No")<<endl;}
void possible(bool a){ cout<<(a?"possible":"impossible")<<endl; }
void Possible(bool a){ cout<<(a?"Possible":"Impossible")<<endl; }
void POSSIBLE(bool a){ cout<<(a?"POSSIBLE":"IMPOSSIBLE")<<endl; }
template<class T>void print(T a){cout<<a<<endl;}
template<class T>auto min(const T& a){ return *min_element(all(a)); }
template<class T>auto max(const T& a){ return *max_element(all(a)); }
template<class T,class F>void print(pair<T,F> a){cout<<a.fi<<" "<<a.se<<endl;}
template<class T>bool chmax(T &a, const T &b) { if (a<b) { a=b; return 1; } return 0;}
template<class T>bool chmin(T &a, const T &b) { if (b<a) { a=b; return 1; } return 0;}
template<class T> void ifmin(T t,T u){if(t>u){cout<<-1<<endl;}else{cout<<t<<endl;}}
template<class T> void ifmax(T t,T u){if(t>u){cout<<-1<<endl;}else{cout<<t<<endl;}}
ll fastgcd(ll u,ll v){ll shl=0;while(u&&v&&u!=v){bool eu=!(u&1);bool ev=!(v&1);if(eu&&ev){++shl;u>>=1;v>>=1;}else if(eu&&!ev){u>>=1;}else if(!eu&&ev){v>>=1;}else if(u>=v){u=(u-v)>>1;}else{ll tmp=u;u=(v-u)>>1;v=tmp;}}return !u?v<<shl:u<<shl;}
ll modPow(ll a, ll n, ll mod) { if(mod==1) return 0;ll ret = 1; ll p = a % mod; while (n) { if (n & 1) ret = ret * p % mod; p = p * p % mod; n >>= 1; } return ret; }
vector<ll> divisor(ll x){ vector<ll> ans; for(ll i = 1; i * i <= x; i++){ if(x % i == 0) {ans.push_back(i); if(i*i!=x){ ans.push_back(x / ans[i]);}}}sor(ans); return ans; }
ll pop(ll x){return __builtin_popcountll(x);}
ll poplong(ll x){ll y=-1;while(x){x/=2;y++;}return y;}
P hyou(P a){ll x=fastgcd(abs(a.fi),abs(a.se));a.fi/=x;a.se/=x;if(a.se<0){a.fi*=-1;a.se*=-1;}return a;}
P Pplus(P a,P b){ return hyou({a.fi*b.se+b.fi*a.se,a.se*b.se});}
P Ptimes(P a,ll b){ return hyou({a.fi*b,a.se});}
P Ptimes(P a,P b){ return hyou({a.fi*b.fi,a.se*b.se});}
P Pminus(P a,P b){ return hyou({a.fi*b.se-b.fi*a.se,a.se*b.se});}
P Pgyaku(P a){ return hyou({a.se,a.fi});}

void cincout(){
  ios::sync_with_stdio(false);
    std::cin.tie(nullptr);
  cout<< fixed << setprecision(15);
}
template<class T>
vector<T> NTT(vector<T> a,vector<T> b){
  ll nmod=T::mod();
  int n=a.size();
  int m=b.size();
  vector<int> x1(n);
  vector<int> y1(m);
  for(int i=0;i<n;i++){
    ll tmp1,tmp2,tmp3;
    tmp1=a[i].val();
    x1[i]=tmp1;
  }
  for(int i=0;i<m;i++){
    ll tmp1,tmp2,tmp3;
    tmp1=b[i].val();
    y1[i]=tmp1;
  }
  auto z1=convolution<167772161>(x1,y1);
  auto z2=convolution<469762049>(x1,y1);
  auto z3=convolution<1224736769>(x1,y1);
  vector<T> res(n+m-1);
  ll m1=167772161;
  ll m2=469762049;
  ll m3=1224736769;
  ll m1m2=104391568;
  ll m1m2m3=721017874;
  ll mm12=m1*m2%nmod;
  for(int i=0;i<n+m-1;i++){
    int v1=(z2[i]-z1[i])*m1m2%m2;
    if(v1<0) v1+=m2;
    int v2=(z3[i]-(z1[i]+v1*m1)%m3)*m1m2m3%m3;
    if(v2<0) v2+=m3;
    res[i]=(z1[i]+v1*m1+v2*mm12);
  }
  return res;
}
enum Mode {
	FAST = 1,
	NAIVE = -1,
};
template <class T, Mode mode = FAST>
struct FormalPowerSeries : std::vector<T> {
	using std::vector<T>::vector;
	using std::vector<T>::size;
	using std::vector<T>::resize;
	using F = FormalPowerSeries;
  F &operator+=(const F &g){
    for(int i=0;i<int(min((*this).size(),g.size()));i++){
      (*this)[i]+=g[i];
    }
    return *this;
  }
  F &operator+=(const T &t){
    assert(int((*this).size()));
    (*this)[0]+=t;
    return *this;
  }
  F &operator-=(const F &g) {
    for(int i=0;i<int(min((*this).size(),g.size()));i++){
      (*this)[i]-=g[i];
    }
    return *this;
  }
  F &operator-=(const T &t){
    assert(int((*this).size()));
    (*this)[0]-=t;
    return *this;
  }
  F &operator*=(const T &g) {
    for(int i=0;i<int((*this).size());i++){
      (*this)[i]*=g;
    }
    return *this;
  }
  F &operator/=(const T &g) {
    T div=g.inv();
    for(int i=0;i<int((*this).size());i++){
      (*this)[i]*=div;
    }
    return *this;
  }
  F &operator<<=(const int d) {
    int n=(*this).size();
    (*this).insert((*this).begin(),d,0);
    (*this).resize(n);
    return *this;
  }
  F &operator>>=(const int d) {
    int n=(*this).size();
    (*this).erase((*this).begin(),(*this).begin()+min(n, d));
    (*this).resize(n);
    return *this;
  }
  F &operator=(const std::vector<T> &v) {
    int n = (*this).size();
    for(int i = 0; i < n; ++i) (*this)[i] = v[i];
    return *this;
  }
  F operator-() const {
    F ret = *this;
    return ret * -1;
  }
  F &operator*=(const F &g) {
      int n=(*this).size();
      auto tmp=NTT(*this,g);
      int k=tmp.size();
      (*this).resize(k);
      for(int i=0;i<k;++i){
        (*this)[i]=tmp[i];
      }
      return *this;
  }
  F &operator/=(const F &g) {
  if(mode == FAST){
  int n = (*this).size();
  (*this) = atcoder::convolution(*this, g.inv());
  return *this;
  }
  else{
  int n = (*this).size();
  (*this) = NTT(*this, g.inv());
  return *this;
  }
  }
  
  F &operator%=(const F &g) { return *this-=*this/g*g; }
  F operator*(const T &g) const { return F(*this)*=g;}
  F operator-(const T &g) const { return F(*this)-=g;}
  F operator*(const F &g) const { return F(*this)*=g;}
  F operator-(const F &g) const { return F(*this)-=g;}
  F operator+(const F &g) const { return F(*this)+=g;}
  F operator/(const F &g) const { return F(*this)/=g;}
  F operator%(const F &g) const { return F(*this)%=g;}
  F operator<<(const int d) const { return F(*this)<<=d;}
  F operator>>(const int d) const { return F(*this)>>=d;}  
  
  void onemul(const int d,const T c){
    int n=(*this).size();
    for(int i=n-d-1;i>=0;i--){
      (*this)[i+d]+=(*this)[i]*c;
    }
  }
  void onediv(const int d,const T c){
    int n=(*this).size();
    for(int i=0;i<n-d;i++){
      (*this)[i+d]-=(*this)[i]*c;
    }
  }
  T eval(const T &t) const {
  int n = (*this).size();
  T res = 0, tmp = 1;
  for(int i = 0; i < n; ++i){
  res += (*this)[i] * tmp, tmp *= t;
  }
  return res;
  }
  F inv(int deg = -1) const {
  int n = (*this).size();
  if(mode==FAST){
  if(deg == -1) deg = n;
  assert(deg > 0);
  F res{(*this)[0].inv()};
  while(int(res.size()) < deg) {
  int m = res.size();
  F f((*this).begin(), (*this).begin() + std::min(n, m * 2)), r(res);
  f.resize(m * 2), atcoder::internal::butterfly(f);
  r.resize(m * 2), atcoder::internal::butterfly(r);
  for(int i = 0; i < m * 2; ++i) f[i] *= r[i];
  atcoder::internal::butterfly_inv(f);
  f.erase(f.begin(), f.begin() + m);
  f.resize(m * 2), atcoder::internal::butterfly(f);
  for(int i = 0; i < m * 2; ++i) f[i] *= r[i];
  atcoder::internal::butterfly_inv(f);
  T iz = T(m * 2).inv();
  iz *= -iz;
  for(int i = 0; i < m; ++i) f[i] *= iz;
  res.insert(res.end(), f.begin(), f.begin() + m);
  }
  res.resize(deg);
  return res;
  }
  else{
    assert(n!=0&&(*this)[0]!=0);
    if(deg==-1) deg=n;
    assert(deg>0);
    F res{(*this)[0].inv()};
    while(res.size()<deg){
      int m=res.size();
      F f(begin(*this),begin(*this)+min(n,2*m));
      F r(res);
      f.resize(2*m);
      r.resize(2*m);
      vector<T> s=NTT(f,r);
      s.resize(2*m);
      for(int i=0;i<2*m;i++){
        s[i]=-s[i];
      }
      s[0]+=2;
      vector<T> g=NTT(s,r);
      g.resize(2*m);
      swap(res,g);
    }
    res.resize(n);
    return res;
  }
  }
  F &diff_inplace() {
  int n = (*this).size();
  for(int i = 1; i < n; ++i) (*this)[i - 1] = (*this)[i] * i;
  (*this)[n - 1] = 0;
  return *this;
  }
  F diff() const { F(*this).diff_inplace();}
  F &integral_inplace() {
  int n = (*this).size(), mod = T::mod();
  std::vector<T> inv(n);
  {
  inv[1] = 1;
  for(int i = 2; i < n; ++i)
  inv[i] = T(mod) - inv[mod % i] * (mod / i);
  }
  for(int i = n - 2; i >= 0; --i) (*this)[i + 1] = (*this)[i] * inv[i + 1];
  (*this)[0] = 0;
  return *this;
  }
  F integral() const { return F(*this).integral_inplace(); }
  F &log_inplace() {
  int n = (*this).size();
  assert(n and (*this)[0] == 1);
  F f_inv = (*this).inv();
  (*this).diff_inplace();
  (*this) *= f_inv;
  (*this).integral_inplace();
  return *this;
  }
  F log() const { return F(*this).log_inplace(); }
  F &deriv_inplace() {
  int n = (*this).size();
  assert(n);
  for(int i = 2; i < n; ++i) (*this)[i] *= i;
 (*this).erase((*this).begin());
 (*this).push_back(0);
 return *this;
 }
 F deriv() const { return F(*this).deriv_inplace(); }
 F &exp_inplace() {
 int n = (*this).size();
 assert(n and (*this)[0] == 0);
 F g{1};
 (*this)[0] = 1;
 F h_drv((*this).deriv());
 for(int m = 1; m < n; m *= 2) {	
 F f((*this).begin(), (*this).begin() + m);
 f.resize(2 * m), atcoder::internal::butterfly(f);
 auto mult_f = [&](F &p) {
 p.resize(2 * m);
 atcoder::internal::butterfly(p);
 for(int i = 0; i < 2 * m; ++i) p[i] *= f[i];
 atcoder::internal::butterfly_inv(p);
 p /= 2 * m;
 };
 if(m > 1) {
 F g_(g);
 g_.resize(2 * m), atcoder::internal::butterfly(g_);
 for(int i = 0; i < 2 * m; ++i) g_[i] *= g_[i] * f[i];
 atcoder::internal::butterfly_inv(g_);
 T iz = T(-2 * m).inv();
 g_ *= iz;
 g.insert(g.end(), g_.begin() + m / 2, g_.begin() + m);
 }
 F t((*this).begin(), (*this).begin() + m);
 t.deriv_inplace();
 {
 F r{h_drv.begin(), h_drv.begin() + m - 1};
 mult_f(r);
 for(int i = 0; i < m; ++i) t[i] -= r[i] + r[m + i];
 }
 t.insert(t.begin(), t.back());
 t.pop_back();
 t *= g;
 F v((*this).begin() + m, (*this).begin() + std::min(n, 2 * m));
 v.resize(m);
 t.insert(t.begin(), m - 1, 0);
 t.push_back(0);
 t.integral_inplace();
 for(int i = 0; i < m; ++i) v[i] -= t[m + i];
 mult_f(v);
 for(int i = 0; i < std::min(n - m, m); ++i)
 (*this)[m + i] = v[i];
 }
 return *this;
 }
 F exp() const { return F(*this).exp_inplace(); }
 F &pow_inplace(long long k) {
 int n = (*this).size(), l = 0;
 assert(k >= 0);
 if(!k){
 for(int i = 0; i < n; ++i) (*this)[i] = !i;
 return *this;
 }
 while(l < n and (*this)[l] == 0) ++l;
 if(l > (n - 1) / k or l == n) return *this = F(n);
 T c = (*this)[l];
 (*this).erase((*this).begin(), (*this).begin() + l);
 (*this) /= c;
 (*this).log_inplace();
 (*this).resize(n - l * k);
 (*this) *= k;
 (*this).exp_inplace();
 (*this) *= c.pow(k);
 (*this).insert((*this).begin(), l * k, 0);
 return *this;
 }
 F pow(const long long k) const { return F(*this).pow_inplace(); }
 void manymul(vector<pair<int, T>> g) {
    int n = (*this).size();
    auto [d, c] = g.front();
    if (d == 0) g.erase(g.begin());
    else c = 0;
    drep(i, n) {
      (*this)[i] *= c;
      for (auto &[j, b] : g) {
        if (j > i) break;
        (*this)[i] += (*this)[i-j] * b;
      }
    }
  }
 void manydiv(vector<pair<int, T>> g) {
    int n = (*this).size();
    auto [d, c] = g.front();
    assert(d == 0 && c != T(0));
    T ic = c.inv();
    g.erase(g.begin());
    rep(i, 0,n) {
      for (auto &[j, b] : g) {
        if (j > i) break;
        (*this)[i] -= (*this)[i-j] * b;
      }
      (*this)[i] *= ic;
    }
  }
};
 
template<class T>
void GaussJordan(vector<vector<T>> &A,bool is_extended = false){
  ll m=A.size(),n=A[0].size();
  ll rank=0;
  for(int i=0;i<n;i++){
    if(is_extended&&i==n-1) break;
    ll p=-1;
    for(int j=rank;j<m;j++){
      if(A[j][i]!=T(0)){
        p=j;
        break;
      }
    }
    if(p==-1) continue;
    swap(A[p],A[rank]);
    auto k=A[rank][i];
    for(int i2=0;i2<n;i2++){
      A[rank][i2]/=k;
    }
    for(int j=0;j<m;j++){
      if(j!=rank&&A[j][i]!=T(0)){
        auto fac=A[j][i];
        for(int i2=0;i2<n;i2++){
          A[j][i2]-=A[rank][i2]*fac;
        }
      }
    }
    rank++;
  }
}
 
template<class T>
void linear_equation(vector<vector<T>> a, vector<T> b, vector<T> &res) {
  ll m=a.size(),n=a[0].size();
  vector<vector<T>> M(m,vector<T>(n+1));
  for(int i=0;i<m;i++){
    for(int j=0;j<n;j++){
      M[i][j]=a[i][j];
    }
    M[i][n]=b[i];
  }
  GaussJordan(M,true);
  res.assign(n,0);
  for(int i=0;i<n;i++) res[i]=M[i][n];
}
template<class F>
pair<F,F> Characteristic_equation(const F &a) {
  using T=typename F::value_type;
  ll n=a.size();
  ll p=n/2;
  ll u=p+(p+1);
  vector<vector<T>> f(u,vector<T>(u));
  f[0][0]=1;
  for(int i=1;i<=p;i++){
    f[i][i-1]=-1;
  }
  for(int i=p;i<u;i++){
    ll t=0;
    for(int j=1+i-p;j<u;j++){
      f[j][i]=a[t];
      t++;
    }
  }
  vector<T> b(u);
  b[0]=1;
  vector<T> res(u);
  linear_equation(f,b,res);
  F X(p),Y(p+1);
  for(int i=0;i<p;i++) X[i]=res[i];
  for(int j=p;j<res.size();j++) Y[j-p]=res[j];
  return {X,Y};
}
template <class T, Mode mode>
T getK(FormalPowerSeries<T, mode> p, FormalPowerSeries<T, mode> q,ll k){
  if(k<0) return T(0);
  ll d=q.size();
  while(k){
    auto qn=q;
    for(int i=1;i<d;i+=2) qn[i]*=-1;
    p.resize(2*d);
    q.resize(2*d);
    p*=qn;
    q*=qn;
    for(int i=0;i<d-1;i++){
      p[i]=p[(i<<1)|(k&1)];
    }
    for(int i=0;i<d;i++){
      q[i]=q[(i<<1)];
    }
    p.resize(d-1);
    q.resize(d);
    k/=2;
  }
  return p[0];
}
using mint = modint;
using fps = FormalPowerSeries<mint,NAIVE>;
/*using mint = modint998244353;
using fps = FormalPowerSeries<atcoder::modint998244353,FAST>;*/
/*fps TaylorShift(fps f,mint c){
  for(int i=0;i<n;i++){
    f[i]*=fac[i];
  }
  fps g(n);
  for(int i=0;i<n;i++){
    g[n-i-1]=c.pow(i)*finv[i];
  }
  g*=f;
  fps res(n);
  for(int i=0;i<n;i++){
    res[i]=g[n+i-1]*finv[i];
  }
  return res;
}*/
int main() {
  cincout();
  mint::set_mod(1000000009);
  fps f(1),g(1000);
  f[0]=1;
  g[0]=1;
  {
    fps a(1000);
    a[0]=1;
    a[1]=-1;
    g*=a;
  }
  {
    fps a(1000);
    a[0]=1;
    a[5]=-1;
    g*=a;
  }
  {
    fps a(1000);
    a[0]=1;
    a[10]=-1;
    g*=a;
  }
  {
    fps a(1000);
    a[0]=1;
    a[50]=-1;
    g*=a;
  }
  {
    fps a(1000);
    a[0]=1;
    a[100]=-1;
    g*=a;
  }
  {
    fps a(1000);
    a[0]=1;
    a[500]=-1;
    g*=a;
  }
  ll t;
  cin>>t;
  g.resize(667);
  while(t--){
    ll a;
    cin>>a;
    cout<<getK(f,g,a).val()<<endl;
  }
}