#include using namespace std; namespace { using ull = unsigned long long; using ll = long long; #define endl "\n" #define REP(i, n) for (ll i = 0; i < n; i++) #define REPR(i, n) for (ll i = n; i >= 0; i--) #define FOR(i, m, n) for (ll i = m; i < n; i++) #define even(x) (x) % 2 == 0 #define odd(x) (x) % 2 != 0 #define all(x) (x).begin(), (x).end() #define rall(x) (x).rbegin(), (x).rend() #define pcnt __builtin_popcount #define buli(x) __builtin_popcountll(x) #define UNIQUE(v) v.erase(unique(v.begin(), v.end()), v.end()); #define inp(t, x) \ t x; \ cin >> x; #define ithBit(n, i) ((n) >> (i)&1) #define INIT() \ cin.tie(0); \ ios::sync_with_stdio(0); \ cout << fixed << setprecision(20) // these functions return the position of result of Binary Search. #define LB(s, t, x) (int)(lower_bound(s, t, x) - s) #define UB(s, t, x) (int)(upper_bound(s, t, x) - s) #define M_PI 3.14159265358979323846 ll qp(ll a, ll b, int mo) { ll ans = 1; do { if (b & 1) ans = 1ll * ans * a % mo; a = 1ll * a * a % mo; } while (b >>= 1); return ans; } ll gcd(ll a, ll b) { return b ? gcd(b, a % b) : a; } ll lcm(ll a, ll b) { ll temp = gcd(a, b); return temp ? (a / temp * b) : 0; } int mDays[] = {31, 29, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31}; int dx[4] = {1, 0, -1, 0}, dy[4] = {0, 1, 0, -1}; int dx8[] = {1, -1, 0, 0, 1, 1, -1, -1}, dy8[] = {0, 0, -1, 1, -1, 1, -1, 1}; template class #if defined(__has_cpp_attribute) && __has_cpp_attribute(nodiscard) [[nodiscard]] #elif defined(__GNUC__) && __GNUC_PREREQ(3, 4) __attribute__((warn_unused_result)) #endif // defined(__has_cpp_attribute) && __has_cpp_attribute(nodiscard) FixPoint : F { public : explicit constexpr FixPoint(F &&f) noexcept : F(std::forward(f)) {} template constexpr decltype(auto) operator()(Args &&... args) const { return F::operator()(*this, std::forward(args)...); } // namespace } ; // class FixPoint template static inline constexpr decltype(auto) makeFixPoint(F &&f) noexcept { return FixPoint{std::forward(f)}; } template vector make_v(size_t a) { return vector(a); } template auto make_v(size_t a, size_t b, Ts... ts) { return vector(b, ts...))>(a, make_v(b, ts...)); } template typename enable_if::value != 0>::type fill_v(U &u, const V... v) { u = U(v...); } template typename enable_if::value == 0>::type fill_v(U &u, const V... v) { for (auto &e : u) fill_v(e, v...); } template bool chmax(T &a, const T &b) { if (a < b) { a = b; return 1; } return 0; } template bool chmin(T &a, const T &b) { if (b < a) { a = b; return 1; } return 0; } inline bool rangeCheck2D(int nx, int ny, int Width, int Height) { return nx >= 0 and nx < Width and ny >= 0 and ny < Height; } ll i_query(set x, set y) { cout << x.size() << " " << y.size() << " "; for (const auto &e : x) cout << e << " "; for (const auto &e : y) cout << e << " "; cout << endl; fflush(stdout); ll ret; cin >> ret; return ret; } void i_answer(ll ans, ll d) { cout << "-1 " << ans << endl; fflush(stdout); } } // namespace namespace { #define DUMPOUT cerr #ifndef DEBUG_ #define dump(...) #else #define dump(...) \ DUMPOUT << " "; \ DUMPOUT << #__VA_ARGS__ << " :[" << __LINE__ << ":" << __FUNCTION__ << "]" << endl; \ DUMPOUT << " "; \ dump_func(__VA_ARGS__) #endif void dump_func() { DUMPOUT << endl; } template void dump_func(Head &&head, Tail &&... tail) { DUMPOUT << head; if (sizeof...(Tail) == 0) { DUMPOUT << " "; } else { DUMPOUT << ", "; } dump_func(std::move(tail)...); } template ostream &operator<<(ostream &os, const vector &v) { for (auto i = begin(v); i != end(v); ++i) os << *i << (i == end(v) - 1 ? "" : " "); return os; } template void out2Dvector(vector v) { for (const auto &vv : v) cout << vv << endl; } template istream &operator>>(istream &is, vector &v) { for (auto i = begin(v); i != end(v); ++i) is >> *i; return is; } template ostream &operator<<(ostream &os, pair &pair_var) { os << "(" << pair_var.first << ", " << pair_var.second << ")"; return os; } template ostream &operator<<(ostream &os, map &map_var) { os << "{"; for (auto itr = map_var.begin(); itr != map_var.end(); itr++) { os << "(" << itr->first << ", " << itr->second << ")"; itr++; if (itr != map_var.end()) os << ", "; itr--; } os << "}"; return os; } template ostream &operator<<(ostream &os, set &set_var) { os << "{"; for (auto itr = set_var.begin(); itr != set_var.end(); itr++) { os << *itr; ++itr; if (itr != set_var.end()) os << ", "; itr--; } os << "}"; return os; } } // namespace /* lambda expression auto f = [](int arg1, double arg2) { return ret; }; lambda recursion auto result = makeFixPoint([&](auto rec, int pos, int v) -> int { rec(pos, v); })(0, 1); auto func = makeFixPoint([]() -> int {}); int ret = func(); tuple binding auto [x, y] = make_tuple(0, 0); for pair auto [a, b] = pair({v1, v2}); bitset bs(ini_val); // N must be constant bs.reset(); // reset all */ // modint namespace { template struct Fp { long long val; constexpr Fp(long long v = 0) noexcept : val(v % MODULO) { if (val < 0) v += MODULO; } constexpr Fp operator-() const noexcept { return val ? MODULO - val : 0; } constexpr Fp operator+(const Fp &r) const noexcept { return Fp(*this) += r; } constexpr Fp operator-(const Fp &r) const noexcept { return Fp(*this) -= r; } constexpr Fp operator*(const Fp &r) const noexcept { return Fp(*this) *= r; } constexpr Fp operator/(const Fp &r) const noexcept { return Fp(*this) /= r; } constexpr Fp &operator+=(const Fp &r) noexcept { val += r.val; if (val >= MODULO) val -= MODULO; return *this; } constexpr Fp &operator++(int) noexcept { val++; if (val >= MODULO) val -= MODULO; return *this; } constexpr Fp &operator++() noexcept { val; if (val >= MODULO) val -= MODULO; return *this; } constexpr Fp &operator-=(const Fp &r) noexcept { val -= r.val; if (val < 0) val += MODULO; return *this; } constexpr Fp &operator*=(const Fp &r) noexcept { val = val * r.val % MODULO; return *this; } constexpr Fp &operator/=(const Fp &r) noexcept { long long a = r.val, b = MODULO, u = 1, v = 0; while (b) { long long t = a / b; a -= t * b; swap(a, b); u -= t * v; swap(u, v); } val = val * u % MODULO; if (val < 0) val += MODULO; return *this; } constexpr bool operator==(const Fp &r) const noexcept { return this->val == r.val; } constexpr bool operator!=(const Fp &r) const noexcept { return this->val != r.val; } }; template constexpr ostream &operator<<(ostream &os, const Fp &x) noexcept { return os << x.val; } template constexpr istream &operator>>(istream &is, Fp &x) noexcept { return is >> x.val; } template // nlogn constexpr Fp modpow(const Fp &a, long long n) noexcept { if (n == 0) return 1; auto t = modpow(a, n / 2); t = t * t; if (n & 1) t = t * a; return t; } const int MAX = 510000; const int MOD = 1000000007; using mint = Fp; // 1≤k≤n≤10^7 class BinomLib { public: vector fac, finv, inv; BinomLib() { fac = vector(MAX); finv = vector(MAX); inv = vector(MAX); fac[0] = fac[1] = 1; finv[0] = finv[1] = 1; inv[1] = 1; for (int i = 2; i < MAX; i++) { fac[i] = fac[i - 1] * mint(i); inv[i] = -inv[MOD % i] * mint(MOD / i); finv[i] = finv[i - 1] * inv[i]; } } mint nCr(int n, int k) { if (n < k) return 0; if (n < 0 || k < 0) return 0; return fac[n] * finv[k] * finv[n - k]; } // number of cases to divide n objects into k groups mint nHr(int n, int k) { if (n == 0 and k == 0) return 1; return nCr(n + k - 1, n); } }; } int main(void) { INIT(); // comment out for Interective Program inp(ll, N); inp(ll, K); BinomLib bl; mint res = 0; REP(i, K + 1) { mint tmp = bl.nCr(K, i) * modpow(mint(i), N); if ( (K-i) & 1 ) res -= tmp; else res += tmp; } cout << res << endl; return 0; } //*/