#include #include #include using namespace std; using int128 = __int128_t; #define rep(i, n) for (int i = 0; i < n; ++i) #define reps(i, n, s) for (int i = 0; i < n; i += s) #define repl(i, l, r) for (int i = l; i < r; ++i) #define repsl(i, l, r, s) for (int i = l; i < r; i += s) #define all(iterable) (iterable).begin(), (iterable).end() constexpr int dx4[4] = {1, 0, -1, 0}; constexpr int dy4[4] = {0, 1, 0, -1}; constexpr int dx8[8] = {1, 1, 0, -1, -1, -1, 0, 1}; constexpr int dy8[8] = {0, 1, 1, 1, 0, -1, -1, -1}; template void print(const vector& vec, const string sep = " ", const string end = "\n") { int n = vec.size(); rep(i, n) { cout << vec[i]; if (i < n - 1) cout << sep; else cout << end; } } template void read(vector& a, int begin_index, int length) { if (a.size() < begin_index + length) a.resize(begin_index + length); while (length --> 0) cin >> a[begin_index++]; } template void read(vector& a) { read(a, 0, a.size()); } template class modint { public: modint(): _v(0) {} template modint(T x) { T v = x % mod; if (v < 0) v += mod; _v = v; } unsigned int val() const { return _v; } modint& operator+=(const modint& x) { _v = add(_v, x._v); return *this; } modint& operator-=(const modint& x) { _v = sub(_v, x._v); return *this; } modint& operator*=(const modint& x) { _v = mul(_v, x._v); return *this; } modint& operator/=(const modint& x) { _v = mul(_v, inv(x._v)); return *this; } friend modint operator+(const modint& x, const modint& y) { return modint(x) += y; } friend modint operator-(const modint& x, const modint& y) { return modint(x) -= y; } friend modint operator*(const modint& x, const modint& y) { return modint(x) *= y; } friend modint operator/(const modint& x, const modint& y) { return modint(x) /= y; } modint& operator++() { ++_v; if (_v == mod) _v = 0; return *this; } modint& operator--() { if (_v == 0) _v = mod; --_v; return *this; } modint operator++(int) { modint res = modint(_v); ++*this; return res; } modint operator--(int) { modint res = modint(_v); --*this; return res; } modint operator+() const { return modint(_v); } modint operator-() const { return modint(mod - _v); } bool operator==(const modint& x) const { return _v == x._v; } bool operator!=(const modint& x) const { return _v != x._v; } bool operator!() const noexcept { return _v > 0; } modint inv() const { return inv(_v); } modint pow(long long x, bool accept_negative_power = false) const { bool negative_power = false; if (accept_negative_power) { if (x < 0) { negative_power = true; x = -x; } } else { assert(x >= 0); } modint res = 1, pw2 = _v; for (; x > 0; x >>= 1) { if (x & 1) res *= pw2; pw2 *= pw2; } return negative_power ? 1 / res : res; } static constexpr unsigned int safe_mod(const long long v) { long long z = v % (long long) mod; if (z < 0) z += mod; return (unsigned int) z; } private: unsigned int _v; static constexpr unsigned int add(const unsigned int x, const unsigned int y) { unsigned int z = x + y; if (z >= mod) z -= mod; return z; } static constexpr unsigned int sub(const unsigned int x, const unsigned int y) { return x < y ? x + mod - y : x - y; } static constexpr unsigned int mul(const unsigned int x, const unsigned int y) { return (unsigned int) ((unsigned long long) x * y % mod); } static constexpr unsigned int inv(const unsigned int x) { long long a = x, b = mod, u = 1, v = 0; long long tmp; while (b) { long long t = a / b; a -= t * b; tmp = a; a = b; b = tmp; u -= t * v; tmp = u; u = v; v = tmp; } return safe_mod(u); } }; template class factorial { public: factorial(size_t initial_max) : _sz(initial_max + 1) { _fac.resize(_sz); _fac_inv.resize(_sz); _fac[0] = _fac_inv[0] = 1; additional_calc(1, _sz); } const T& fac(const size_t i) { ensure_size(i + 1); return _fac[i]; } const U& fac_inv(const size_t i) { ensure_size(i + 1); return _fac_inv[i]; } U binom(const int n, const int r) { if (n < 0 or r < 0 or n < r) return 0; ensure_size(n + 1); return _fac[n] * _fac_inv[r] * _fac_inv[n - r]; } U perm(const int n, const int r) { if (n < 0 or r < 0 or n < r) return 0; ensure_size(n + 1); return _fac[n] * _fac_inv[n - r]; } private: size_t _sz; std::vector _fac; std::vector _fac_inv; void additional_calc(const size_t l, const size_t r) { assert(l > 0); for (size_t i = l; i < r; ++i) _fac[i] = _fac[i - 1] * i; _fac_inv[r - 1] = (U) 1 / _fac[r - 1]; for (size_t i = r - 1; i > l; --i) _fac_inv[i - 1] = _fac_inv[i] * i; } void ensure_size(const size_t sz) { if (sz < _sz) return; size_t new_size = std::max(sz, _sz * 2); _fac.resize(new_size); _fac_inv.resize(new_size); additional_calc(_sz, new_size); _sz = new_size; } }; using mint = modint<1000000007>; int main() { int n; long long m; cin >> n >> m; --n, --m; vector a(n); read(a); factorial fac(n); mint num = m + 1; mint ans = 0; rep(k, n) { ans += a[n - k - 1] * num * fac.fac_inv(k + 1); num *= (m + k + 2); } cout << ans.val() << '\n'; return 0; }