#include using namespace std; #define rep(i,n) for (int i=0;i<(n);i++) #define rep2(i,a,b) for (int i=(a);i<(b);i++) #define rrep(i,n) for (int i=(n)-1;i>=0;i--) #define rrep2(i,a,b) for (int i=(b)-1;i>=(a);i--) #define all(a) (a).begin(),(a).end() typedef long long ll; typedef pair P; typedef vector vi; typedef vector

vp; typedef vector vll; typedef vector Vec; typedef vector Mat; const ll mod = 1e9 + 7; Mat mulMatMat(Mat A, Mat B) { int n = A.size(); Mat C(n, Vec(n, 0)); rep(i, n) { rep(j, n) { rep(k, n) { C[i][j] += A[i][k] * B[k][j]; C[i][j] %= mod; } } } return C; } Vec mulMatVec(Mat A, Vec vec) { int n = A.size(); Vec res(n, 0); reverse(all(vec)); // 添え字の大きい要素を上に持ってくるため rep(i, n) { rep(j, n) { res[i] += A[i][j] * vec[j]; res[i] %= mod; } } return res; } Mat powMat(Mat A, ll p) { int n = A.size(); Mat R(n, Vec(n, 0)); rep(i, n) R[i][i] = 1; // 単位行列 for (; p >= 1; p /= 2) { if (p & 1) { R = mulMatMat(A, R); } A = mulMatMat(A, A); } return R; } signed main() { std::ios::sync_with_stdio(false); std::cin.tie(0); ll N, K; cin >> N >> K; vll a(N); rep(i, N) cin >> a[i]; if (N <= (ll)1e4 && K <= (ll)1e6) { vll f(K); ll t = 0; rep(i, N) { f[i] = a[i]; t += f[i]; t %= mod; } rep2(i, N, K) { f[i] = t; t = (t + mod - f[i - N]) % mod; t += f[i]; t %= mod; } ll s = 0; rep(i, K) { s += f[i]; s %= mod; } cout << f[K - 1] << " " << s << endl; } else { // Sを行列累乗で計算 Mat A(N + 1, Vec(N + 1, 0)); A[0][0] = 2; A[0][N] = -1 + mod; rep2(i, 1, N + 1) A[i][i-1] = 1; // 初期ベクトル s を計算しておく Vec f(N + 1, 0); rep(i, N) f[i] = a[i]; rep(i, N) f[N] += f[i]; Vec s(N + 1, 0); rep(i, N + 1) s[i] = f[i]; rep(i, N) s[i + 1] += s[i]; A = powMat(A, K - (N + 1)); s = mulMatVec(A, s); // s[k], s[k-1], ... cout << (s[0] - s[1] + mod) % mod << " " << s[0] << endl; } } // // Fを直接計算する場合 // Mat A(N, Vec(N, 0)); // rep(i, N) A[0][i] = 1; // rep2(i, 1, N) A[i][i - 1] = 1; // // auto B = powMat(A, K - N); // auto vec = mulMatVec(B, a); // ll fk = vec[0]; // for (auto x : vec) { // cout << x << " "; // } // cout << endl; // // cout << fk << endl;