#include using namespace std; #define all(c) ((c).begin()), ((c).end()) #define dump(c) cerr << "> " << #c << " = " << (c) << endl; #define iter(c) __typeof((c).begin()) #define tr(i, c) for (iter(c) i = (c).begin(); i != (c).end(); i++) #define REP(i, a, b) for (int i = a; i < (int)(b); i++) #define rep(i, n) REP(i, 0, n) #define mp make_pair #define fst first #define snd second #define pb push_back #define debug(fmt, ...) \ fprintf( stderr, \ fmt "\n", \ ##__VA_ARGS__ \ ) typedef unsigned int uint; typedef long long ll; typedef unsigned long long ull; typedef vector vi; typedef vector vll; typedef vector vvll; typedef vector vvi; typedef vector vd; typedef vector vvd; typedef vector vs; typedef pair pii; typedef pair pll; const int INF = 1 << 29; const double EPS = 1e-10; double zero(double d) { return d < EPS ? 0.0 : d; } template bool chmax(T &a, const T &b) { if (a < b) { a = b; return true; } return false; } template bool chmin(T &a, const T &b) { if (b < a) { a = b; return true; } return false; } #define UNIQUE(v) v.erase( unique(v.begin(), v.end()), v.end() ); template ostream &operator<<(ostream &os, const pair &p) { return os << '(' << p.first << ',' << p.second << ')'; } template ostream &operator<<(ostream &os, const vector &a) { os << '['; rep(i, a.size()) os << (i ? " " : "") << a[i]; return os << ']'; } string toString(int i) { stringstream ss; ss << i; return ss.str(); } const int MOD = 1000000007; // a^k ll fpow(ll a, ll k, int M) { ll res = 1ll; ll x = a; while (k != 0) { if ((k & 1) == 1) res = (res * x) % M; x = (x * x) % M; k >>= 1; } return res; } struct prepare { prepare() { cout.setf(ios::fixed, ios::floatfield); cout.precision(8); ios_base::sync_with_stdio(false); } } _prepare; vvi mul(vvi &mat, vvi &mat2, int M) { int H = mat.size(), W = mat[0].size(); vvi ans(H, vi(W, 0)); rep(r, H) { rep(c, W) { rep(i, W) { ans[r][c] += ((ll) mat[r][i] * mat2[i][c]) % M; ans[r][c] %= M; } } } return ans; } vi mul(vvi &mat, vi &vec, int M) { int H = mat.size(), W = mat[0].size(); vi ans(W, 0); rep(r, H) { rep(c, W) { ans[r] += ((ll) mat[r][c] * vec[c]) % M; ans[r] %= M; } } return ans; } // a^k vvi fpow(vvi a, ll k, int M) { vvi res(a.size(), vi(a[0].size(), 0)); rep(i, a.size()) res[i][i] = 1; vvi x = a; while (k != 0) { if ((k & 1) == 1) res = mul(res, x, M); x = mul(x, x, M); k >>= 1; } return res; } int main() { ll N, K; cin >> N >> K; // case 1 if (K <= (int) (1e6) + 100) { vi dp(K, 0); ll sum = 0; rep(i, N) { cin >> dp[i]; sum += dp[i]; sum %= MOD; } dp[N] = sum; ll total = sum + sum; total %= MOD; REP(i, N + 1, K) { sum = ((ll)sum - dp[i - N - 1] + MOD) % MOD; sum = ((ll)sum + dp[i - 1]) % MOD; dp[i] = sum; total += dp[i]; total %= MOD; } cout << dp[K - 1] << " " << total << endl; } // case 2 else { vi nums(N + 1); int t = 0; rep(i, N) { cin >> nums[i]; t += nums[i]; } nums[N] = t; vvi mat(N + 1, vi(N + 1, 0)); rep(c, N) mat[0][c] = 1; REP(r, 1, N) { rep(c, N) mat[r][c] = mat[r - 1][c] * 2; mat[r][r - 1]--; } rep(c, N) rep(r, N) mat[N][c] += mat[r][c]; mat[N][N] = 1; vvi muled = fpow(mat, K / N, MOD); vi ans = mul(muled, nums, MOD); int pos = (K % N); cout << ans[(pos - 1 + N) % N] << " "; ll total = ans[N]; REP(i, pos, N) total = (total - ans[i] + MOD) % MOD; cout << total << endl; } return 0; }