/** * @FileName a.cpp * @Author kanpurin * @Created 2020.05.23 01:51:04 **/ #include "bits/stdc++.h" using namespace std; typedef long long ll; constexpr int MOD = 1e9 + 7; struct mint { private: long long x; public: mint(long long x = 0) : x((MOD + x) % MOD) {} mint(std::string &s) { long long z = 0; for (int i = 0; i < s.size(); i++) { z *= 10; z += s[i] - '0'; z %= MOD; } this->x = z; } mint &operator+=(const mint &a) { if ((x += a.x) >= MOD) x -= MOD; return *this; } mint &operator-=(const mint &a) { if ((x += MOD - a.x) >= MOD) x -= MOD; return *this; } mint &operator*=(const mint &a) { (x *= a.x) %= MOD; return *this; } mint &operator/=(const mint &a) { long long n = MOD - 2; mint u = 1, b = a; while (n > 0) { if (n & 1) { u *= b; } b *= b; n >>= 1; } return *this *= u; } mint operator+(const mint &a) const { mint res(*this); return res += a; } mint operator-(const mint &a) const { mint res(*this); return res -= a; } mint operator*(const mint &a) const { mint res(*this); return res *= a; } mint operator/(const mint &a) const { mint res(*this); return res /= a; } friend std::ostream &operator<<(std::ostream &os, const mint &n) { return os << n.x; } bool operator==(const mint &a) const { return this->x == a.x; } }; template < class T > struct Matrix { std::vector< std::vector< T > > A; Matrix() {} Matrix(size_t n, size_t m) : A(n, std::vector< T >(m, 0)) {} Matrix(size_t n) : A(n, std::vector< T >(n, 0)){}; size_t height() const { return (A.size()); } size_t width() const { return (A[0].size()); } inline const std::vector< T > &operator[](int k) const { return (A.at(k)); } inline std::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()); std::vector< std::vector< T > > C(n, std::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+(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); } friend std::ostream &operator<<(std::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); } // 行列式 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); } // k乗 // 元の数は変更されない Matrix pow(ll k) const { auto res = I(A.size()); auto M = *this; while (k > 0) { if (k & 1) { res *= M; } M *= M; k >>= 1; } return res; } }; int main() { ll n, k; cin >> n >> k; if (n >= 31) { vector< int > a(n); vector< mint > b(k), s(k); mint sum = 0; for (int i = 0; i < n; i++) { cin >> a[i]; sum += a[i]; b[i] = a[i]; if (i - 1 >= 0) s[i] = s[i - 1] + b[i]; else s[i] = b[i]; } for (int i = n; i < k; i++) { b[i] = sum; sum += b[i] - b[i - n]; s[i] = s[i - 1] + b[i]; } cout << b[k - 1] << " " << s[k - 1] << endl; } else { mint ans = 0; vector< int > a(n); for (int i = 0; i < n; i++) { cin >> a[i]; } for (int i = 0; i < n - 2; i++) { ans += mint(a[i]) * (n - 1 - (i + 1)); } //cout << "1:" << ans << endl; ans -= a[n - 1]; //cout << "2:" << ans << endl; Matrix< mint > mat(n); for (int i = 0; i < n; i++) { mat.A[0][i] = 1; } for (int i = 1; i < n; i++) { for (int j = 0; j < n; j++) { if (i == j + 1) { mat.A[i][j] = 1; } else { mat.A[i][j] = 0; } } } auto v = mat.pow(k + 1 - n); for (int i = 0; i < n; i++) { ans += v.A[0][i] * a[n - 1 - i]; } mint ans2 = 0; v = mat.pow(k - n); for (int i = 0; i < n; i++) { ans2 += v.A[0][i] * a[n - 1 - i]; } //cout << "3:" << ans << endl; for (ll i = k - n + 2; i <= k; i++) { if (i <= n) { ans += a[i - 1] * (n-k-1+i); } v = mat.pow(i - n); for (int j = 0; j < n; j++) { ans += v.A[0][j] * a[n - 1 - j] * (n-k-1+i); } } cout << ans2 << " " << ans / (n-1) << endl; } return 0; }