#pragma GCC optimize("O2") #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #define whlie while #define mp make_pair #define pb emplace_back #define fi first #define se second #define inf 1001001001 #define infLL ( (1LL << 61)) #define FOR(i,a,b) for(int (i)=((int)a); (i)<((int)b); (i)++) // [a,b) #define rep(i,N) FOR((i), 0, ((int)N)) // [0,N) #define FORR(i,a,b) for(int (i)=((int)b) - 1; (i)>=((int)a); (i)--) #define repr(i,N) FORR((i), 0, ((int)N)) #define all(v) (v).begin(),(v).end() #define sz(v) ((int)(v).size()) #define vrep(v,it) for(auto it=v.begin();it!=v.end();it++) #define vrepr(v,it) for(auto it=v.rbegin();it!=v.rend();it++) #define inx(t,...) t __VA_ARGS__; in(__VA_ARGS__) #define ini(...) int __VA_ARGS__; in(__VA_ARGS__) #define inl(...) ll __VA_ARGS__; in(__VA_ARGS__) #define inc(...) char __VA_ARGS__; in(__VA_ARGS__) #define ins(...) string __VA_ARGS__; in(__VA_ARGS__) #define ind(...) double __VA_ARGS__; in(__VA_ARGS__) #define inpii(...) pii __VA_ARGS__; in(__VA_ARGS__) #define invi(v,...) vi v; in(v,##__VA_ARGS__) #define invl(v,...) vl v; in(v,##__VA_ARGS__) #define mem(ar,val) memset((ar), (val), sizeof(ar) ) #define mem0(ar) memset((ar), 0, sizeof(ar) ) #define mem1(ar) memset((ar), -1, sizeof(ar) ) #ifdef LOCAL #define dbg(...) fprintf(stderr, __VA_ARGS__) #define trc(...) do { cout << #__VA_ARGS__ << " = "; dbg_out(__VA_ARGS__);} while(0) #define stopif(val) assert( !(val) ) #define vdbg(v,...) do { cout << #v << " = "; vector_debug(v , ##__VA_ARGS__);} while(0) #else #define dbg(...) 1 #define trc(...) 1 #define stopif(...) 1 #define vdbg(...) 1 #endif using namespace std; typedef long long ll; typedef pair pii; typedef pair pll; typedef vector vi; typedef vector vl; typedef vector vs; typedef vector vpii; typedef vector< vector > vvi; struct IoSetup { IoSetup() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(15); cerr << fixed << setprecision(15); } } iosetup; int gcd(int a, int b){if(a>b) swap(a,b); return a==0 ? b : gcd(b%a,a);} ll gcd(ll a, ll b){if(a>b) swap(a,b); return a==0 ? b : gcd(b%a,a);} int lcm(int a, int b){return (a / gcd(a,b)) * b;} ll lcm(ll a, ll b){return (a / gcd(a,b)) * b;} inline ll pow(int a, int b){ll ans = 1; rep(i,b) ans *= a; return ans;} inline ll pow(ll a, ll b){ll ans = 1; rep(i,b) ans*= a; return ans;} inline ll pow(int a, ll b){ll ans = 1; rep(i,b) ans *= a; return ans;} inline ll pow(ll a, int b){ll ans = 1; rep(i,b) ans*= a; return ans;} template inline bool amin(T &x, U y) { return (y < x) ? (x = y, true) : false; } template inline bool amax(T &x, U y) { return (x < y) ? (x = y, true) : false; } template inline void _cin(C &c){cin >> c;} template inline void _cin(pair &p){cin >> p.fi; cin >> p.se;} template inline void _cout(const C &c){cout << c;} template inline void _cout(const pair &p){cout << p.fi << ' ' << p.se;} void in(){} template void in(T &t,U &...u){ _cin(t); in(u...);} void out(){cout << "\n";} template void out(const T &t,U ...u){ _cout(t); if(sizeof...(u)) cout << ' '; out(u...);} template inline void in(vector &v,int N=-1){if(sz(v) != 0){int M=(N == -1) ? sz(v) : N; rep(i,M) _cin(v[i]);}else{C c;rep(i,N) v.pb((_cin(c),c));}} template inline void in(C v[],int N){rep(i,N) _cin(v[i]);} template inline void out(const vector &v,int N=-1){int M=(N == -1) ? sz(v) : N; rep(i,M) {cout<<( (i)?" ":"" ); _cout(v[i]);} cout<<"\n";} template inline void out(C v[],int N){rep(i,N) {cout<<( (i)?" ":"" ); _cout(v[i]);} cout<<"\n";} template inline void vector_debug(const vector &v,int N=-1){cout << "{"; int M=(N == -1) ? sz(v) : N; rep(i,M) {cout<<( (i)?", ":"" ); _cout(v[i]);} cout<<"}"< inline void vector_debug(C v[], int N){cout << "{"; rep(i,N) {cout<<((i)?", ":""); _cout(*(v+i));} cout<<"}"< void dbg_out(const T &t,U ...u){ _cout(t); if(sizeof...(u)) cout << ", "; dbg_out(u...);} template void dbg_out(const vector &v,U ...u){vector_debug(v); if(sizeof...(u)) cout << ", "; dbg_out(u...);} template void dbg_out(const vector> &v,U ...u){cout << "{ "; rep(i,sz(v)) {if(i)cout<<", "; vector_debug(v[i]);} cout << " }"; if(sizeof...(u)) cout << ", "; dbg_out(u...);} template inline C vmax(const vector &v){C n=v[0]; rep(i,sz(v)) amax(n,v[i]); return n;} template inline C vmax(C v[], int N){C n=v[0]; rep( i , N ) amax(n,v[i]); return n;} template inline C vmin(const vector &v){C n=v[0]; rep(i,sz(v)) amin(n,v[i]); return n;} template inline C vmin(C v[], int N){C n=v[0]; rep( i , N ) amin(n,v[i]); return n;} template inline C vsum(const vector &v){C n=0; rep(i,sz(v)) n+=v[i]; return n;} template inline C vsum(C v[], int N){C n=0; rep( i , N ) n+=v[i]; return n;} //////////// /// main /// //////////// template< int mod > struct ModInt { int x; ModInt() : x(0) {} ModInt(int64_t y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {} ModInt &operator+=(const ModInt &p) { if((x += p.x) >= mod) x -= mod; return *this; } ModInt &operator-=(const ModInt &p) { if((x += mod - p.x) >= mod) x -= mod; return *this; } ModInt &operator*=(const ModInt &p) { x = (int) (1LL * x * p.x % mod); return *this; } ModInt &operator/=(const ModInt &p) { *this *= p.inverse(); return *this; } ModInt operator-() const { return ModInt(-x); } ModInt operator+(const ModInt &p) const { return ModInt(*this) += p; } ModInt operator-(const ModInt &p) const { return ModInt(*this) -= p; } ModInt operator*(const ModInt &p) const { return ModInt(*this) *= p; } ModInt operator/(const ModInt &p) const { return ModInt(*this) /= p; } bool operator==(const ModInt &p) const { return x == p.x; } bool operator!=(const ModInt &p) const { return x != p.x; } ModInt inverse() const { int a = x, b = mod, u = 1, v = 0, t; while(b > 0) { t = a / b; swap(a -= t * b, b); swap(u -= t * v, v); } return ModInt(u); } ModInt pow(int64_t n) const { ModInt ret(1), mul(x); while(n > 0) { if(n & 1) ret *= mul; mul *= mul; n >>= 1; } return ret; } friend ostream &operator<<(ostream &os, const ModInt &p) { return os << p.x; } friend istream &operator>>(istream &is, ModInt &a) { int64_t t; is >> t; a = ModInt< mod >(t); return (is); } }; template< class T > struct Matrix { vector< vector< T > > A; Matrix() {} Matrix(size_t n, size_t m) : A(n, vector< T >(m, 0)) {} Matrix(size_t n) : A(n, vector< T >(n, 0)) {}; size_t height() const { return (A.size()); } size_t width() const { return (A[0].size()); } inline const vector< T > &operator[](int k) const { return (A.at(k)); } inline vector< T > &operator[](int k) { return (A.at(k)); } static Matrix I(size_t n) { Matrix mat(n); for(int i = 0; i < n; i++) mat[i][i] = 1; return (mat); } Matrix &operator+=(const Matrix &B) { size_t n = height(), m = width(); assert(n == B.height() && m == B.width()); for(int i = 0; i < n; i++) for(int j = 0; j < m; j++) (*this)[i][j] += B[i][j]; return (*this); } Matrix &operator-=(const Matrix &B) { size_t n = height(), m = width(); assert(n == B.height() && m == B.width()); for(int i = 0; i < n; i++) for(int j = 0; j < m; j++) (*this)[i][j] -= B[i][j]; return (*this); } Matrix &operator*=(const Matrix &B) { size_t n = height(), m = B.width(), p = width(); assert(p == B.height()); vector< vector< T > > C(n, vector< T >(m, 0)); for(int i = 0; i < n; i++) for(int j = 0; j < m; j++) for(int k = 0; k < p; k++) C[i][j] = (C[i][j] + (*this)[i][k] * B[k][j]); A.swap(C); return (*this); } Matrix &operator^=(long long k) { Matrix B = Matrix::I(height()); while(k > 0) { if(k & 1) B *= *this; *this *= *this; k >>= 1LL; } A.swap(B.A); return (*this); } Matrix operator+(const Matrix &B) const { return (Matrix(*this) += B); } Matrix operator-(const Matrix &B) const { return (Matrix(*this) -= B); } Matrix operator*(const Matrix &B) const { return (Matrix(*this) *= B); } Matrix operator^(const long long k) const { return (Matrix(*this) ^= k); } friend ostream &operator<<(ostream &os, Matrix &p) { size_t n = p.height(), m = p.width(); for(int i = 0; i < n; i++) { os << "["; for(int j = 0; j < m; j++) { os << p[i][j] << (j + 1 == m ? "]\n" : ","); } } return (os); } T determinant() { Matrix B(*this); assert(width() == height()); T ret = 1; for(int i = 0; i < width(); i++) { int idx = -1; for(int j = i; j < width(); j++) { if(B[j][i] != 0) idx = j; } if(idx == -1) return (0); if(i != idx) { ret *= -1; swap(B[i], B[idx]); } ret *= B[i][i]; T vv = B[i][i]; for(int j = 0; j < width(); j++) { B[i][j] /= vv; } for(int j = i + 1; j < width(); j++) { T a = B[j][i]; for(int k = 0; k < width(); k++) { B[j][k] -= B[i][k] * a; } } } return (ret); } }; using Modint = ModInt<1000000007>; template Matrix Mpow(Matrix A, ll N){ if(N == 0){ return A.I(A.height()); } if(N == 1) return A; if(N % 2 == 1) return (Mpow(A, N - 1) * A); Matrix half = Mpow(A , N / 2); return (half * half); } int main(){ constexpr ll mod = 1000000007; inl(N); inl(K); vl A(N + 1); FOR(i, 1, N + 1) in(A[i]); if(K <= N || N > 30){ vl F(K + 10,0),S(K + 10,0); FOR(i,1,N + 1){ F[i] = A[i]; S[i] = S[i - 1] + A[i]; } if( K <= N ) {out(F[K],S[K]); return 0;}; FOR( i , N + 1, K + 1 ){ F[i] = ( S[i - 1] - S[i - N - 1] + mod ) % mod; S[i] = (S[i - 1] + F[i]) % mod; } out(F[K],S[K]); return 0; } Matrix FM(N); rep(i,N) FM[0][i] = 1; rep(i,N-1) FM[i+1][i] = 1; //cout << FM; Matrix F(N,1); rep(i,N) F[i][0] = A[N - i]; Matrix SM(N + 1); SM[0][0] = 2; SM[0][N] = -1; rep(i,N) SM[i+1][i] = 1; Matrix S(N + 1, 1); FOR(i,1,N + 1){ S[N - i][0] = S[N - i + 1][0] + A[i]; } Matrix ans = Mpow(FM , K - N) * F; //cout << ans; Matrix ans2 = Mpow(SM, K - N) * S; out(ans[0][0] , ans2[0][0]); }