#ifndef LOCAL #pragma GCC optimize ("O3") #pragma GCC optimize ("unroll-loops") #pragma GCC target ("avx") #endif #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; using ll = long long; using VI = vector; using VVI = vector>; using VLL = vector; using VVLL = vector>; using VB = vector; using PII = pair; using PLL = pair; template using minheap = priority_queue, greater>; const int INF = 1000000007; const ll INF_LL = 1'000'000'000'000'000'007; #define __overload3(_1, _2, _3, name,...) name #define rep(...) __overload3(__VA_ARGS__, repFromUntil, repUntil, repeat)(__VA_ARGS__) #define repeat(times) repFromUntil(_name##__LINE__, 0, times) #define repUntil(name, times) repFromUntil(name, 0, times) #define repFromUntil(name, from, until) for (int name = from, name##__until = (until); name < name##__until; name++) #define repr(...) __overload3(__VA_ARGS__, reprFromUntil, reprUntil, repeat)(__VA_ARGS__) #define reprUntil(name, times) reprFromUntil(name, 0, times) #define reprFromUntil(name, from, until) for (int name = (until) - 1, name##__from = (from); name >= name##__from; name--) #define EXIT(out) do { OUT(out); exit(0); } while (0) #define all(x) begin(x), end(x) #define rall(x) rbegin(x), rend(x) #ifdef LOCAL #define debug(v) do {debugos << "L" << __LINE__ << " " << #v << " > ";debugos<<(v)< ";for(auto e:(v)){debugos< ";for(int x=0;x<(w);x++){debugos<<(m)[x]<<" ";}debugos< \n";for(int y=0;y<(h);y++){for(int x=0;x<(w);x++){debugos<<(m)[y][x]<<" ";}debugos< bool chmin(T& var, U x) { if (var > x) { var = x; return true; } else return false; } template bool chmax(T& var, U x) { if (var < x) { var = x; return true; } else return false; } template int sgn(T val) { return (T(0) < val) - (val < T(0)); } ll power(ll e, int t, ll mod = INF_LL) { ll res = 1; while (t) { if (t&1) res = (res * e) % mod; t >>= 1; e = (e * e) % mod; } return res; } template T divceil(T m, T d) { assert(m >= 0 and d > 0); return (m+d-1)/d; } template vector make_v(size_t a, T b) { return vector(a, b); } template auto make_v(size_t a, Ts... ts) { return vector(a, make_v(ts...)); } string operator*(const string& s, int times) { string res = ""; rep(times) res += s; return res; } struct Edge { int to; ll cost; Edge(int _to): to(_to), cost(1) {} Edge(int _to, ll _cost): to(_to), cost(_cost) {} operator int() { return to; } }; using Graph = vector>; class MyScanner { public: int offset = 0; char nc(){ #ifdef LOCAL return getchar(); #else static char buf[100000],*L=buf,*R=buf; return L==R&&(R=(L=buf)+fread(buf,1,100000,stdin),L==R)?EOF:*L++; #endif } template void input_integer(T& var) { var = 0; T sign = 1; int cc = nc(); for (; cc<'0' || '9'>(char& var) { var = c(); return *this; } MyScanner& operator>>(int& var) { input_integer(var); return *this; } MyScanner& operator>>(ll& var) { input_integer(var); return *this; } MyScanner& operator>>(string& var) { var = ""; int cc = nc(); for (; !isvisiblechar(cc); cc = nc()); for (; isvisiblechar(cc); cc = nc()) var.push_back(cc); return *this; } template operator T() { T x; *this >> x; return x; } template void operator()(T &t) { *this >> t; } template void operator()(T &t, Ts &...ts) { *this >> t; this->operator()(ts...); } template void iter(Iter first, Iter last) { while (first != last) *this >> *first, first++; } VI vi(int n) { VI res(n); iter(all(res)); return res; } VVI vvi(int n, int m) { VVI res(n); rep(i, n) res[i] = vi(m); return res; } VLL vll(int n) { VLL res(n); iter(all(res)); return res; } VVLL vvll(int n, int m) { VVLL res(n); rep(i, n) res[i] = vll(m); return res; } template vector v(int n) { vector res(n); iter(all(res)); return res; } private: int isvisiblechar(int c) { return 0x21 <= c && c <= 0x7E; } } IN, IN1{-1}; class MyPrinter { public: int offset = 0; template void output_integer(T var) { var += offset; if (var == 0) { putchar('0'); return; } if (var < 0) putchar('-'), var = -var; char stack[32]; int stack_p = 0; while (var) stack[stack_p++] = '0' + (var % 10), var /= 10; while (stack_p) putchar(stack[--stack_p]); } MyPrinter& operator<<(char c) { putchar(c); return *this; } MyPrinter& operator<<(double x) { printf("%.10f", x); return *this; } template MyPrinter& operator<<(T var) { output_integer(var); return *this; } MyPrinter& operator<<(char* str_p) { while (*str_p) putchar(*(str_p++)); return *this; } MyPrinter& operator<<(const char* str_p) { while (*str_p) putchar(*(str_p++)); return *this; } MyPrinter& operator<<(const string& str) { const char* p = str.c_str(); const char* l = p + str.size(); while (p < l) putchar(*p++); return *this; } template void operator()(T x) { *this << x << newl; } template void operator()(T x, Ts ...xs) { *this << x << " "; this->operator()(xs...); } template void iter(Iter s, Iter t) { if (s == t) *this << "\n"; else for (; s != t; s++) *this << *s << " \n"[next(s, 1) == t]; } template void range(const Range& r) { iter(begin(r), end(r)); } } OUT, OUT1{1}; class DebugPrint { public: template DebugPrint& operator <<(const T& v) { #ifdef LOCAL cerr << v; #endif return *this; } } debugos; template OutStream& operator<<(OutStream& out, const pair& var) { return out << var.first << " " << var.second; } template * = nullptr> OutStream& tuple_impl(OutStream& out, const Tuple& var) { return out; } template * = nullptr> OutStream& tuple_impl(OutStream& out, const Tuple& var) { out << get(var) << " "; return tuple_impl(out, var); } template OutStream& operator<<(OutStream& out, const tuple& var) { return tuple_impl, 0, sizeof...(Ts)>(out, var); } template InStream& operator>>(InStream& in, pair& var) { return in >> var.first >> var.second; } template * = nullptr> InStream& tuple_impl(InStream& in, Tuple& var) { return in; } template * = nullptr> InStream& tuple_impl(InStream& in, Tuple& var) { in >> get(var); return tuple_impl(in, var); } template InStream& operator>>(InStream& in, tuple& var) { return tuple_impl, 0, sizeof...(Ts)>(in, var); } class modint; constexpr modint pow(modint, size_t); constexpr ll MOD = 1000000007; class modint { public: ll value; constexpr modint(const ll x = 0) noexcept : value(x) { value %= MOD; if (value < 0) value += MOD; } constexpr bool operator==(const modint& rhs) { return value == rhs.value; } constexpr bool operator!=(const modint& rhs) { return value != rhs.value; } constexpr modint operator-() const { return modint(0) - *this; } 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) { value += rhs.value; if (value >= MOD) value -= MOD; return *this; } constexpr modint &operator-=(const modint& rhs) { if (value < rhs.value) value += MOD; value -= rhs.value; return *this; } constexpr modint &operator*=(const modint& rhs) { value = value * rhs.value % MOD; return *this; } constexpr modint &operator/=(const modint& rhs) { return *this *= pow(rhs, MOD - 2); } constexpr modint &operator++() { return *this += 1; } constexpr modint operator++(int) { modint tmp(*this); ++(*this); return tmp; } constexpr modint &operator--() { return *this -= 1; } constexpr modint operator--(int) { modint tmp(*this); --(*this); return tmp; } constexpr operator int() const { return (int)value; } constexpr operator ll() const { return value; } }; template OutStream& operator<<(OutStream& out, modint n) { out << n.value; return out; } template InStream& operator>>(InStream& in, modint& n) { ll var; in >> var; n = modint(var); return in; } constexpr modint pow(modint base, size_t exp) { modint res = 1; while (exp) { if (exp % 2) res *= base; base *= base; exp /= 2; } return res; } // O(r + log MOD) modint choose(int n, int r) { chmin(r, n-r); if (r < 0) return modint(0); modint nu = 1, de = 1; rep(i, r) nu *= n-i, de *= i+1; return nu / de; } class binomial { public: vector fact, invfact; binomial(int n) : fact(n+1), invfact(n+1) { fact[0] = 1; rep(i, n) fact[i+1] = fact[i] * modint(i+1); invfact[n] = modint(1) / fact[n]; repr(i, n) invfact[i] = invfact[i+1] * modint(i+1); } modint operator()(int n, int r) { chmin(r, n-r); if (r < 0) return modint(0); return fact[n] * invfact[r] * invfact[n-r]; } }; int main() { int n = IN, m = IN; modint res = 0; binomial binom(m+100); rep(i, 1, m+1) { modint k = pow(modint(i), n) * binom(m, i); if ((m-i)%2 == 0) res += k; else res -= k; } OUT(res); }