#include #include using namespace std; typedef vector VI; typedef vector VII; const int BUF_LARGE = 10005; const int BUF_SMALL = 35; const int RESULT = 1000005; const int MOD = 1000000007; int N; long long K; int A[BUF_LARGE]; void read() { cin >> N >> K; for (int i = 0; i < N; ++i) cin >> A[i]; } VII matmul(const VII &a, const VII &b) { VII ret = VII(a.size(), VI(b[0].size())); for (int i = 0; i < a.size(); ++i) for (int j = 0; j < b[0].size(); ++j) for (int k = 0; k < a[0].size(); ++k) ret[i][j] = (ret[i][j] + 1LL * a[i][k] * b[k][j]) % MOD; return ret; } VII matpow(VII &p, long long e) { if (e == 0) { VII vii = VII(p.size(), VI(p.size())); for (int i = 0; i < p.size(); ++i) vii[i][i] = 1; return vii; } VII t = matpow(p, e / 2); if (e & 1) return matmul(p, matmul(t, t)); else return matmul(t, t); } void work() { if (N <= 30) { // calc F(K) VII p = VII(N, VI(N)); for (int i = 0; i < N; ++i) p[0][i] = 1; for (int r = 1, c = 0; r < N; ++r, ++c) p[r][c] = 1; VII ret = matpow(p, K - N); int ans = 0; for (int i = 0; i < N; ++i) ans = (ans + 1LL * ret[0][i] * A[N - i - 1]) % MOD; cout << ans << ' '; // calc S(K) p = VII(N + 1, VI(N + 1)); p[0][0] = 2; p[0][N] = MOD - 1; for (int r = 1, c = 0; r < N + 1; ++r, ++c) p[r][c] = 1; ret = matpow(p, K - N); int sum = 0; for (int i = 0; i < N; ++i) sum = (sum + A[i]) % MOD; ans = 0; for (int i = 0; i < N; ++i) { ans = (ans + 1LL * ret[0][i] * sum) % MOD; sum = (sum + MOD - A[N - 1 - i]) % MOD; } cout << ans << endl; } else { static int result[RESULT]; for (int i = 0; i < N; ++i) result[i] = A[i]; int sum = 0; int sk = 0; for (int i = 0; i < N; ++i) { sum = (sum + A[i]) % MOD; sk = (sk + A[i]) % MOD; } for (int i = N; i < K; ++i) { result[i] = sum; sk = (sk + sum) % MOD; sum = (1LL * sum + sum + MOD - result[i - N]) % MOD; } cout << result[K - 1] << ' ' << sk << endl; } } int main() { read(); work(); return 0; }