This documentation is automatically generated by online-judge-tools/verification-helper
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// verification-helper: PROBLEM https://yukicoder.me/problems/22 #include<bits/stdc++.h> using namespace std; #define call_from_test #include "../../mod/mint.cpp" #include "../../polynomial/lagrangeinterpolation.cpp" #undef call_from_test signed main(){ cin.tie(0); ios::sync_with_stdio(0); using M = Mint<int, int(1e9+9)>; const int MAX = 666 * 6 + 10; vector<M> dp(MAX,0); dp[0]=M(1); for(int x:{1,5,10,50,100,500}) for(int j=x;j<MAX;j++) dp[j]+=dp[j-x]; int T; cin>>T; while(T--){ using ll = long long; ll m; cin>>m; vector<M> ys(6); for(int i=0;i<6;i++) ys[i]=dp[(m%500)+(i*500)]; cout<<lagrange_interpolation(ys,M(m/500))<<"\n"; } cout<<flush; return 0; }
#line 1 "test/yukicoder/0022.test.cpp" // verification-helper: PROBLEM https://yukicoder.me/problems/22 #include<bits/stdc++.h> using namespace std; #define call_from_test #line 1 "mod/mint.cpp" #line 3 "mod/mint.cpp" using namespace std; #endif //BEGIN CUT HERE template<typename T, T MOD = 1000000007> struct Mint{ inline static constexpr T mod = MOD; T v; Mint():v(0){} Mint(signed v):v(v){} Mint(long long t){v=t%MOD;if(v<0) v+=MOD;} Mint pow(long long k){ Mint res(1),tmp(v); while(k){ if(k&1) res*=tmp; tmp*=tmp; k>>=1; } return res; } static Mint add_identity(){return Mint(0);} static Mint mul_identity(){return Mint(1);} Mint inv(){return pow(MOD-2);} Mint& operator+=(Mint a){v+=a.v;if(v>=MOD)v-=MOD;return *this;} Mint& operator-=(Mint a){v+=MOD-a.v;if(v>=MOD)v-=MOD;return *this;} Mint& operator*=(Mint a){v=1LL*v*a.v%MOD;return *this;} Mint& operator/=(Mint a){return (*this)*=a.inv();} Mint operator+(Mint a) const{return Mint(v)+=a;} Mint operator-(Mint a) const{return Mint(v)-=a;} Mint operator*(Mint a) const{return Mint(v)*=a;} Mint operator/(Mint a) const{return Mint(v)/=a;} Mint operator+() const{return *this;} Mint operator-() const{return v?Mint(MOD-v):Mint(v);} bool operator==(const Mint a)const{return v==a.v;} bool operator!=(const Mint a)const{return v!=a.v;} static Mint comb(long long n,int k){ Mint num(1),dom(1); for(int i=0;i<k;i++){ num*=Mint(n-i); dom*=Mint(i+1); } return num/dom; } }; template<typename T, T MOD> ostream& operator<<(ostream &os,Mint<T, MOD> m){os<<m.v;return os;} //END CUT HERE #ifndef call_from_test signed main(){ return 0; } #endif #line 1 "polynomial/lagrangeinterpolation.cpp" #line 3 "polynomial/lagrangeinterpolation.cpp" using namespace std; #endif //BEGIN CUT HERE template<typename M> M lagrange_interpolation(vector<M> &y,M t){ int n=y.size()-1; if(t.v<=n) return y[t.v]; vector<M> dp(n+1,1),pd(n+1,1); for(int i=0;i<n;i++) dp[i+1]=dp[i]*(t-M(i)); for(int i=n;i>0;i--) pd[i-1]=pd[i]*(t-M(i)); vector<M> fact(n+1,1),finv(n+1,1); for(int i=1;i<=n;i++) fact[i]=fact[i-1]*M(i); finv[n]=M(1)/fact[n]; for(int i=n;i>=1;i--) finv[i-1]=finv[i]*M(i); M res(0); for(int i=0;i<=n;i++){ M tmp=y[i]*dp[i]*pd[i]*finv[i]*finv[n-i]; if((n-i)&1) res-=tmp; else res+=tmp; } return res; } //END CUT HERE #ifndef call_from_test signed main(){ return 0; } #endif #line 9 "test/yukicoder/0022.test.cpp" #undef call_from_test signed main(){ cin.tie(0); ios::sync_with_stdio(0); using M = Mint<int, int(1e9+9)>; const int MAX = 666 * 6 + 10; vector<M> dp(MAX,0); dp[0]=M(1); for(int x:{1,5,10,50,100,500}) for(int j=x;j<MAX;j++) dp[j]+=dp[j-x]; int T; cin>>T; while(T--){ using ll = long long; ll m; cin>>m; vector<M> ys(6); for(int i=0;i<6;i++) ys[i]=dp[(m%500)+(i*500)]; cout<<lagrange_interpolation(ys,M(m/500))<<"\n"; } cout<<flush; return 0; }