#include #include #include #include #include #include #include #include #include #include #include #include using namespace std; #define rep(i, n) for(int(i) = 0; (i) < (n); (i)++) #define FOR(i, m, n) for(int(i) = (m); (i) < (n); (i)++) #define All(v) (v).begin(), (v).end() #define pb push_back #define MP(a, b) make_pair((a), (b)) using ll = long long; using pii = pair; using pll = pair; const int INF = 1 << 30; const ll LINF = 1LL << 60; const int MOD = 1e9 + 7; template class ModInt { using u64 = uint_fast64_t; public: u64 val; ModInt(const u64 x = 0) : val(x % MOD) {} constexpr u64 &value() { return val; } constexpr ModInt operator-() { return val ? MOD - val : 0; } constexpr ModInt operator+(const ModInt &rhs) const { return ModInt(*this) += rhs; } constexpr ModInt operator-(const ModInt &rhs) const { return ModInt(*this) -= rhs; } constexpr ModInt operator*(const ModInt &rhs) const { return ModInt(*this) *= rhs; } constexpr ModInt operator/(const ModInt &rhs) const { return ModInt(*this) /= rhs; } constexpr ModInt &operator+=(const ModInt &rhs) { val += rhs.val; if(val >= MOD) { val -= MOD; } return *this; } constexpr ModInt &operator-=(const ModInt &rhs) { if(val < rhs.val) { val += MOD; } val -= rhs.val; return *this; } constexpr ModInt &operator*=(const ModInt &rhs) { val = val * rhs.val % MOD; return *this; } constexpr ModInt &operator/=(const ModInt &rhs) { *this *= rhs.inv(); return *this; } constexpr bool operator==(const ModInt &rhs) { return this->a == rhs.a; } constexpr bool operator!=(const ModInt &rhs) { return this->a != rhs.a; } friend constexpr ostream &operator<<(ostream &os, const ModInt &x) { return os << x.val; } friend constexpr istream &operator>>(istream &is, ModInt &x) { return is >> x.val; } constexpr ModInt inv() const { return ModInt(*this).pow(MOD - 2); } constexpr ModInt pow(ll e) const { u64 x = 1, p = val; while(e > 0) { if(e % 2 == 0) { p = (p * p) % MOD; e /= 2; } else { x = (x * p) % MOD; e--; } } return ModInt(x); } }; using mint = ModInt; //二項係数 O(k) // nとkのどちらかが変化するとき、O((n or k) + 変化量)(???)ですべて求められる template T nCk(ll n, ll k, map, T> &mp) { auto key = MP(n, k); if(mp.count(key)) return mp[key]; if(k == 0 || k == n) { T ret = 1; return ret; } if(k == 1 || k == n - 1) { T ret = n; return ret; } // return mp[key] = nCk(n, k - 1, mp) * T(n - k + 1) / T(k); return mp[key] = nCk(n - 1, k, mp) * n / (n - k); } int main() { ll N, K; cin >> N >> K; vector A(N); rep(i, N) cin >> A[i]; mint res = 0; map mp; rep(i, N) { res += nCk(i + K, K, mp) * nCk(N - i + K - 1, K, mp) * A[i]; } cout << res << endl; return 0; }