#pragma region template #pragma GCC optimize("Ofast") #include using namespace std; #ifdef __LOCAL #include #else #define debug(...) void(0) #endif using ll=long long; using ld=long double; using vi=vector; using vll=vector; using pi=pair; using pll=pair; #define overload2(a,b,c,...) c #define overload3(a,b,c,d,...) d #define overload4(a,b,c,d,e,...) e #define overload5(a,b,c,d,e,f,...) f #define TYPE1(T) template #define TYPE2(T,U) template #define TYPE(...) overload2(__VA_ARGS__,TYPE2,TYPE1)(__VA_ARGS__) #define TYPES1(T) template #define TYPES2(H,T) template #define TYPES(...) overload2(__VA_ARGS__,TYPES2,TYPES1)(__VA_ARGS__) #define REP4(i,s,n,d) for(int i=(s);i<(n);i+=(d)) #define REP3(i,s,n) REP4(i,s,n,1) #define REP2(i,n) REP3(i,0,n) #define REP1(n) REP2(tomato,n) #define REP(...) overload4(__VA_ARGS__,REP4,REP3,REP2,REP1)(__VA_ARGS__) #define RREP4(i,s,n,d) for(int i=(n)-1;i>=s;i-=d) #define RREP3(i,s,n) RREP4(i,s,n,1) #define RREP2(i,n) RREP3(i,0,n) #define RREP1(n) RREP2(tomato,n) #define RREP(...) overload4(__VA_ARGS__,RREP4,RREP3,RREP2,RREP1)(__VA_ARGS__) #define ALL(v) v.begin(),v.end() #define RALL(v) v.rbegin(),v.rend() #define SORT(v) sort(ALL(v)) #define RSORT(v) sort(RALL(v)) #define REVERSE(v) reverse(ALL(v)) #define UNIQUE(v) SORT(v),v.erase(unique(ALL(v)),v.end()) TYPES(T) void input(T&... a){ (cin>>...>>a); } #define DECLARE(T,...) T __VA_ARGS__;input(__VA_ARGS__); #define INT(...) DECLARE(int,__VA_ARGS__) #define STR(...) DECLARE(string,__VA_ARGS__) #define LL(...) DECLARE(long long,__VA_ARGS__) #define CHR(...) DECLARE(char,__VA_ARGS__) #define DBL(...) DECLARE(double,__VA_ARGS__) #define VI(n,v) vi v(n);cin>>v; #define VLL(n,v) vll v(n);cin>>v; TYPE(T) istream&operator>>(istream&is,vector&v){ for(auto&a:v)cin>>a; return is; } TYPE(T) ostream&operator<<(ostream&os,const vector&v){ if(&os==&cerr)os<<"["; REP(i,v.size()){ os<>(istream&is,pair&p){ cin>>p.first>>p.second; return is; } TYPE(T) using pq=priority_queue; TYPE(T) using pqg=priority_queue,greater>; TYPE(T) T pick(queue& que){assert(que.size()); T a=que.front();que.pop();return a;} TYPE(T) T pick(pq& que){assert(que.size()); T a=que.top();que.pop();return a;} TYPE(T) T pick(pqg& que){assert(que.size()); T a=que.top();que.pop();return a;} TYPE(T) T pick(stack& sta){assert(sta.size()); T a=sta.top();sta.pop();return a;} string YES(bool f=true){return (f?"YES":"NO");} string Yes(bool f=true){return (f?"Yes":"No");} string yes(bool f=true){return (f?"yes":"no");} constexpr int INF=1e9+7; constexpr ll LINF=ll(1e18)+7; constexpr ld EPS=1e-10; vi iota(int n){vi a(n);iota(ALL(a),0);return a;} TYPE(T) void fin(T a){cout<b&&(a=b,true));} TYPES(T,Ns) auto make_vector(T x,int n,Ns ...ns){ if constexpr(sizeof...(ns)==0)return vector(n,x); else return vector(n,make_vector(x,ns...)); } bool in(const ll S,const int a){return (S>>a)&1;} int popcount(const ll S){return __builtin_popcountll(S);} #pragma endregion template #include #include using namespace atcoder; using mint=modint1000000007; ostream& operator<<(ostream &os,mint a){os<>(istream &is,mint &a){ long long b;is>>b;a=b; return is; } mint op(mint a,mint b){return a+b;} mint e(){return 0;} #define REP_(i,n) for(int i=0;i<(n);i++) #define REP2_(i,s,n) for(int i=(s);i<(n);i++) template struct Matrix{ typedef vector vec; typedef vector mat; size_t r,c; mat M; Matrix(size_t r,size_t c):r(r),c(c),M(r,vec(c,K())){} Matrix(mat A):M(A),r(A.size()),c(A[0].size()){} vec& operator[](size_t k){return M[k];} const vec& operator[](size_t k)const{return M[k];} friend Matrix operator+(const Matrix &A,const Matrix &B){ assert(A.r==B.r&&A.c==B.c); Matrix res(A); REP_(i,A.r)REP_(j,A.c)res[i][j]+=B[i][j]; return res; } Matrix& operator+=(const Matrix &B){ assert(r==B.r&&c==B.c); REP_(i,r)REP_(j,c)M[i][j]+=B[i][j]; return *this; } friend Matrix operator*(const Matrix &A,const Matrix &B){ assert(A.c==B.r); Matrix res(A.r,B.c); REP_(i,A.r)REP_(k,A.c)REP_(j,B.c)res[i][j]+=A[i][k]*B[k][j]; return res; } Matrix& operator*=(const Matrix &B){ M=((*this)*B).M; return *this; } static Matrix I(size_t n){ Matrix res(n,n); REP_(i,n)res[i][i]=K(1); return res; } Matrix pow(long long n)const{ assert(n>=0&&r==c); Matrix A(M),res=I(r); while(n){ if(n&1)res*=A; A*=A; n>>=1; } return res; } int rank() const{ Matrix A(M); int res=0; REP_(k,c){ for(int i=res+1;i30){ segtree seg(k); REP(i,n)seg.set(i,v[i]); REP(i,n,k)seg.set(i,seg.prod(i-n,i)); cout< A(n+1,n+1); REP(i,n)A[0][i]=1; REP(i,1,n)A[i][i-1]=1; A[n][0]=A[n][n]=1; A=A.pow(k-n); Matrix B(n+1,1); REP(i,n)B[i][0]=v[n-1-i]; auto C=A*B; mint ans1=C[0][0]; mint ans2=C[n][0]; REP(i,n-1)ans2+=v[i]; ans2+=ans1; cout<