#include using namespace std; template class y_combinator { F f; public: y_combinator(F&& f) : f(std::forward(f)) {} template auto operator()(Args&&... args) const { return f(*this, std::forward(args)...); } }; constexpr int dx[8] = {1, 0, -1, 0, 1, 1, -1, -1}; constexpr int dy[8] = {0, 1, 0, -1, 1, -1, 1, -1}; using ll = long long; using u32 = unsigned int; using u64 = unsigned long long; using vi = vector; using vl = vector; using pii = pair; using pll = pair; template using vc = vector; template using vvc = vector>; template > using prique = priority_queue, U>; #define overload(a, b, c, d, e, ...) e #define len(x) (ll)(x.size()) #define all(x) (x).begin(), (x).end() #define rall(x) (x).rbegin(), (x).rend() #define rep1(n) for (ll _ = 0; _ < ll(n); _++) #define rep2(i, n) for (ll i = 0; i < ll(n); i++) #define rep3(i, a, b) for (ll i = ll(a); i < ll(b); i++) #define rep4(i, a, b, c) for (ll i = ll(a); i < ll(b); i += ll(c)) #define rep(...) overload(__VA_ARGS__, rep4, rep3, rep2, rep1)(__VA_ARGS__) #define rrep(i, n) for (ll i = ll(n) - 1; i >= 0; i--) template vector cumsum(const vector& a) { vector res(a.size() + 1); rep(i, a.size()) res[i + 1] = res[i] + a[i]; return res; } template void dedup(vector& a) { sort(all(a)), a.erase(unique(all(a)), a.end()); } template bool chmax(T& a, const S& b) { return a < static_cast(b) ? a = static_cast(b), 1 : 0; } template bool chmin(T& a, const S& b) { return a > static_cast(b) ? a = static_cast(b), 1 : 0; } namespace cppio { template struct is_tuple_like : false_type {}; template struct is_tuple_like> : true_type {}; template struct is_tuple_like> : true_type {}; template struct is_container : false_type {}; template struct is_container()))>> : bool_constant, string> && !is_same_v, char*> && !is_same_v, const char*> && !is_array_v>> {}; template void _in(T& x) { if constexpr (is_tuple_like::value) apply([](auto&... elems) { (_in(elems), ...); }, x); else if constexpr (is_container::value) { for (auto& e : x) _in(e); } else cin >> x; } template void _in_all(Ts&... args) { (_in(args), ...); } template void _out(const T& x) { bool first = true; if constexpr (is_tuple_like::value) { apply([&](const auto&... elems) { ((cout << (first ? "" : " "), _out(elems), first = false), ...); }, x); } else if constexpr (is_container::value) { for (const auto& e : x) { if (!first) cout << ' '; _out(e), first = false; } } else cout << x; } template void _print(const Ts&... args) { bool first = true; ((cout << (first ? "" : " "), _out(args), first = false), ...); } template void _out_no_el(const Ts&... args) { _print(args...); } template void _out_all(const Ts&... args) { _out_no_el(args...), cout << '\n'; } } // namespace cppio #define IN(...) cppio::_in_all(__VA_ARGS__) #define OUT(...) cppio::_out_all(__VA_ARGS__) #define INT(...) int __VA_ARGS__; IN(__VA_ARGS__) #define LL(...) ll __VA_ARGS__; IN(__VA_ARGS__) #define STR(...) string __VA_ARGS__; IN(__VA_ARGS__) #define CHR(...) char __VA_ARGS__; IN(__VA_ARGS__) #define DBL(...) double __VA_ARGS__; IN(__VA_ARGS__) #define VEC(type, name, size) vector name(size); IN(name) #define VV(type, name, h, w) vector> name(h, vector(w)); IN(name) #define RETURN(...) do { __VA_ARGS__; return; } while (0) bool Yes(bool b = true) { return OUT(b ? "Yes" : "No"), b; } bool No(bool b = true) { return Yes(!b), b; } bool YES(bool b = true) { return OUT(b ? "YES" : "NO"), b; } bool NO(bool b = true) { return YES(!b), b; } #ifdef ONLINE_JUDGE #define debug(...) (void(0)) #endif template T lagrange_eval(const vector& xs, const vector& ys, const T& X) { assert(xs.size() == ys.size()); int n = xs.size(); for (int i = 0; i < n; i++) { if (xs[i] == X) return ys[i]; } T ans = 0, coef = 1; for (int i = 0; i < n; i++) coef *= X - xs[i]; for (int i = 0; i < n; i++) { T denom = X - xs[i]; for (int j = 0; j < n; j++) { if (i != j) denom *= xs[i] - xs[j]; } ans += ys[i] / denom; } return ans * coef; } template Mint lagrange_eval_ap(const Mint& a, const Mint& d, const vector& ys, const Mint& X) { int n = ys.size(); for (int i = 0; i < n; i++) { if (X == a + d * i) return ys[i]; } Mint ans = 0, pref = 1; vector ifac(n, 1), suff(n + 1, 1); for (int i = 1; i < n; i++) ifac[n - 1] *= i; ifac[n - 1] = 1 / ifac[n - 1]; for (int i = n - 1; i >= 0; i--) { if (i) ifac[i - 1] = ifac[i] * i; suff[i] = suff[i + 1] * (X - a - d * i); } for (int i = 0; i < n; i++) { Mint curr = pref * suff[i + 1] * ifac[i] * ifac[n - 1 - i] * ys[i]; if ((n - 1 - i) & 1) curr = -curr; ans += curr; pref *= X - a - d * i; } ans *= d.pow(n - 1).inv(); return ans; } template Mint lagrange_eval_ap(const vector& ys, const Mint& X) { return lagrange_eval_ap(0, 1, ys, X); } #include using mint = atcoder::modint1000000007; void run_case() { LL(N, K); vector ys(K + 2); mint ans = 0; rep(i, K + 2) { ans += mint::raw(i).pow(K); ys[i] = ans; } OUT(lagrange_eval_ap(ys, N).val()); } int main() { std::ios_base::sync_with_stdio(false); std::cin.tie(nullptr); std::fixed(std::cout).precision(16); int t = 1; while (t--) run_case(); }