This documentation is automatically generated by online-judge-tools/verification-helper
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// verification-helper: PROBLEM https://yukicoder.me/problems/2520 #include<bits/stdc++.h> using namespace std; #define call_from_test #include "../../mod/mint.cpp" #include "../../math/sum_of_geometric_sequence.cpp" #undef call_from_test signed main(){ cin.tie(0); ios::sync_with_stdio(0); using M = Mint<int>; long long n; cin>>n; cout<<M(10).pow(n)+M(3)*sum_of_geometric_sequence(M(10),n)<<endl; return 0; }
#line 1 "test/yukicoder/2520.test.cpp" // verification-helper: PROBLEM https://yukicoder.me/problems/2520 #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 "math/sum_of_geometric_sequence.cpp" #line 3 "math/sum_of_geometric_sequence.cpp" using namespace std; #endif //BEGIN CUT HERE // first: sum_{i=0}^{n-1} r^i // second: r^n template<typename T> pair<T, T> sum_of_geometric_sequence_impl(T r,long long n){ if(n==1) return {T(1),r}; auto p=sum_of_geometric_sequence_impl(r,n/2); T sum=p.first*(T(1)+p.second); T pow=p.second*p.second; if(n&1) sum+=pow,pow*=r; return {sum,pow}; } // sum_{i=0}^{n-1} r^i template<typename T> T sum_of_geometric_sequence(T r,long long n){ return sum_of_geometric_sequence_impl(r,n).first; } //END CUT HERE #ifndef call_from_test //INSERT ABOVE HERE signed main(){ return 0; } #endif #line 9 "test/yukicoder/2520.test.cpp" #undef call_from_test signed main(){ cin.tie(0); ios::sync_with_stdio(0); using M = Mint<int>; long long n; cin>>n; cout<<M(10).pow(n)+M(3)*sum_of_geometric_sequence(M(10),n)<<endl; return 0; }