#include #include using namespace std; using namespace atcoder; istream &operator>>(istream &is, modint &a) { long long v; is >> v; a = v; return is; } ostream &operator<<(ostream &os, const modint &a) { return os << a.val(); } istream &operator>>(istream &is, modint998244353 &a) { long long v; is >> v; a = v; return is; } ostream &operator<<(ostream &os, const modint998244353 &a) { return os << a.val(); } istream &operator>>(istream &is, modint1000000007 &a) { long long v; is >> v; a = v; return is; } ostream &operator<<(ostream &os, const modint1000000007 &a) { return os << a.val(); } typedef long long ll; typedef vector> Graph; typedef pair pii; typedef pair pll; #define rep(i,n) for (int i = 0;i < (int)(n); i++) #define all(x) x.begin(), x.end() #define rall(x) x.rbegin(), x.rend() #define my_sort(x) sort(x.begin(), x.end()) #define my_max(x) *max_element(all(x)) #define my_min(x) *min_element(all(x)) template inline bool chmax(T& a, T b) { if (a < b) { a = b; return 1; } return 0; } template inline bool chmin(T& a, T b) { if (a > b) { a = b; return 1; } return 0; } const int INF = (1<<30) - 1; const ll LINF = (1LL<<62) - 1; const int MOD = 998244353; const int MOD2 = 1e9+7; const double PI = acos(-1); vector di = {1,0,-1,0}; vector dj = {0,1,0,-1}; template void print_2dvector(vector> &vec){ int H = vec.size(); for(int i=0;i void print_vector(vector &vec){ int N = vec.size(); cout << '['; for(int i=0;i # define debug(...) debug_print::multi_print(#__VA_ARGS__, __VA_ARGS__) #else # define debug(...) (static_cast(0)) #endif using mint = modint1000000007; // https://outline.hatenadiary.jp/entry/2020/07/02/205628 template struct Kitamasa{ vector a; // 初期値ベクトル vector d; // 係数ベクトル int k; Kitamasa(vector& a, vector& d) : a(a), d(d), k((int)a.size()) {} // a_n の係数ベクトルを求める vector dfs(ll n){ if(n == k) return d; vector res(k); if(n & 1 || n < k * 2){ vector x = dfs(n - 1); for(int i = 0; i < k; ++i) res[i] = d[i] * x[k - 1]; for(int i = 0; i + 1 < k; ++i) res[i + 1] += x[i]; } else{ vector> x(k, vector(k)); x[0] = dfs(n >> 1); for(int i = 0; i + 1 < k; ++i){ for(int j = 0; j < k; ++j) x[i + 1][j] = d[j] * x[i][k - 1]; for(int j = 0; j + 1 < k; ++j) x[i + 1][j + 1] += x[i][j]; } for(int i = 0; i < k; ++i){ for(int j = 0; j < k; ++j){ res[j] += x[0][i] * x[i][j]; } } } return res; } // a_n を求める T calc(ll n){ vector x = dfs(n); T res = 0; for(int i = 0; i < k; ++i) res += x[i] * a[i]; return res; } }; int main(){ cin.tie(0); ios_base::sync_with_stdio(false); ll N,K; cin >> N >> K; vector a(N); rep(i,N) cin >> a[i]; // vector coef(N+1,0); coef[0] = mint(-1); coef[N] = mint(2); vector b(N+1,0); for(int i=0;i