#include using namespace std; #if __has_include() #include using namespace atcoder; #endif using ll = long long; using ld = long double; using ull = unsigned long long; #define endl "\n" typedef pair 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 #define PQminll priority_queue, greater> #define PQmaxll priority_queue,less> #define PQminP priority_queue, greater

> #define PQmaxP priority_queue,less

> #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; templatevoid vcin(vector &n){for(int i=0;i>n[i];} templatevoid vcin(vector &n,vector &m){for(int i=0;i>n[i]>>m[i];} templatevoid vcout(vector &n){for(int i=0;ivoid vcin(vector> &n){for(int i=0;i>n[i][j];}}} templatevoid vcout(vector> &n){for(int i=0;ivoid print(T a){cout<auto min(const T& a){ return *min_element(all(a)); } templateauto max(const T& a){ return *max_element(all(a)); } templatevoid print(pair a){cout<bool chmax(T &a, const T &b) { if (abool chmin(T &a, const T &b) { if (b void ifmin(T t,T u){if(t>u){cout<<-1< void ifmax(T t,T u){if(t>u){cout<<-1<>=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<>= 1; } return ret; } vector divisor(ll x){ vector 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 vector NTT(vector a,vector b){ ll nmod=T::mod(); int n=a.size(); int m=b.size(); vector x1(n); vector y1(m); for(int i=0;i(x1,y1); auto z2=convolution<469762049>(x1,y1); auto z3=convolution<1224736769>(x1,y1); vector 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 struct FormalPowerSeries : std::vector { using std::vector::vector; using std::vector::size; using std::vector::resize; using F = FormalPowerSeries; F &operator+=(const F &g){ for(int i=0;i>=(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 &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>(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 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() s=NTT(f,r); s.resize(2*m); for(int i=0;i<2*m;i++){ s[i]=-s[i]; } s[0]+=2; vector 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 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> 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> 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 void GaussJordan(vector> &A,bool is_extended = false){ ll m=A.size(),n=A[0].size(); ll rank=0; for(int i=0;i void linear_equation(vector> a, vector b, vector &res) { ll m=a.size(),n=a[0].size(); vector> M(m,vector(n+1)); for(int i=0;i pair 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> f(u,vector(u)); f[0][0]=1; for(int i=1;i<=p;i++){ f[i][i-1]=-1; } for(int i=p;i b(u); b[0]=1; vector res(u); linear_equation(f,b,res); F X(p),Y(p+1); for(int i=0;i T getK(FormalPowerSeries p, FormalPowerSeries q,ll k){ if(k<0) return T(0); ll d=q.size(); while(k){ auto qn=q; for(int i=1;i; /*using mint = modint998244353; using fps = FormalPowerSeries;*/ /*fps TaylorShift(fps f,mint c){ for(int i=0;i dp(1000000); dp[0]=1; vector a={1,5,10,50,100,500}; for(int i=0;i<6;i++){ for(int j=1;j<1000000;j++){ if(j-a[i]>=0) dp[j]+=dp[j-a[i]]; } } ll t; cin>>t; while(t--){ ll a; cin>>a; ll b=a%500; fps f(15); for(int i=0;i<15;i++) f[i]=dp[b+500*i]/dp[b]; auto p=Characteristic_equation(f); cout<<(getK(p.fi,p.se,a/500)*dp[b]).val()<