#include #include using namespace std; const long long MOD = 1e9 + 7; int N; long long K; long long a[10000]; template class _matrix { int _r, _c; vector > _container; public: _matrix(int _r, int _c) : _r(_r), _c(_c), _container(_r, vector(_c)) {} _matrix(int n) : _r(n), _c(n), _container(n, vector(n)) {} _matrix(vector > vec) : _r(vec.size()), _c(vec[0].size()), _container(vec.begin(), vec.end()) {} vector& operator[] (int _r) { return this->_container[_r]; } int r() { return this->_r; } int c() { return this->_c; } /* * return an identity matrix of the size n */ static _matrix eye(int n) { _matrix ret(n); for (int i = 0; i < n; i++) ret[i][i] = 1; return ret; } /* * matrix multiplication */ _matrix operator*(const _matrix &mtx) const { _matrix ret(this->_r, mtx._c); for (int i = 0; i < this->_r; i++) { for (int k = 0; k < this->_c; k++) { for (int j = 0; j < mtx._c; j++) { ret[i][j] += this->_container[i][k] * mtx._container[k][j]; ret[i][j] %= MOD; } } } return ret; } /* * matrix power */ _matrix operator^(long long p) const { _matrix ret = eye(this->_r); _matrix x(this->_container); while (p > 0) { if (p & 1) ret = ret * x; x = x * x; p >>= 1; } return ret; } }; typedef _matrix matrix; void solve1() { matrix A(N+1); A[0][0] = 1; A[0][N-1] = 1; for (int i = 1; i <= N; i++) A[1][i] = 1; for (int i = 2; i <= N; i++) A[i][i-1] = 1; matrix B = A ^ (K-1); vector v(N+1); for (int i = 0; i < N; i++) v[N-i] = a[i]; v[0] = a[0]; long long x = 0; long long y = 0; for (int i = 0; i <= N; i++) { x = (x + B[0][i] * v[i]) % MOD; y = (y + B[N][i] * v[i]) % MOD; } cout << y << " " << x << endl; } long long dp[1000000 + 1]; void solve2() { long long sum = 0; long long acc = 0; for (int i = 0; i < N; i++) dp[i] = a[i], acc = (acc + dp[i]) % MOD; sum = acc; for (int i = N; i < K; i++) { dp[i] = acc; acc = (acc - dp[i-N] + dp[i] + MOD) % MOD; sum = (sum + dp[i]) % MOD; } cout << dp[K-1] << " " << sum << endl; } void solve() { if (K > 1e6) solve1(); else solve2(); } int main() { cin >> N >> K; for (int i = 0; i < N; i++) cin >> a[i]; solve(); return 0; }