#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; using namespace placeholders; using LL = long long; using ULL = unsigned long long; using VI = vector< int >; using VVI = vector< vector< int > >; using VS = vector< string >; using SS = stringstream; using PII = pair< int, int >; using VPII = vector< pair< int, int > >; template < typename T = int > using VT = vector< T >; template < typename T = int > using VVT = vector< vector< T > >; template < typename T = int > using LIM = numeric_limits< T >; template < typename T > inline istream& operator>>( istream &s, vector< T > &v ){ for ( T &t : v ) { s >> t; } return s; } template < typename T > inline ostream& operator<<( ostream &s, const vector< T > &v ){ for ( int i = 0; i < int( v.size() ); ++i ){ s << ( " " + !i ) << v[i]; } return s; } template < typename T > inline T fromString( const string &s ) { T res; istringstream iss( s ); iss >> res; return res; } template < typename T > inline string toString( const T &a ) { ostringstream oss; oss << a; return oss.str(); } #define REP2( i, n ) REP3( i, 0, n ) #define REP3( i, m, n ) for ( int i = ( int )( m ); i < ( int )( n ); ++i ) #define GET_REP( a, b, c, F, ... ) F #define REP( ... ) GET_REP( __VA_ARGS__, REP3, REP2 )( __VA_ARGS__ ) #define FOR( e, c ) for ( auto &&e : c ) #define ALL( c ) begin( c ), end( c ) #define AALL( a, t ) ( t* )a, ( t* )a + sizeof( a ) / sizeof( t ) #define DRANGE( c, p ) ( c ).begin(), ( c ).begin() + ( p ), ( c ).end() #define SZ( v ) ( (int)( v ).size() ) #define EXIST( c, e ) ( ( c ).find( e ) != ( c ).end() ) template < typename T > inline bool chmin( T &a, const T &b ){ if ( b < a ) { a = b; return true; } return false; } template < typename T > inline bool chmax( T &a, const T &b ){ if ( a < b ) { a = b; return true; } return false; } #define PB push_back #define EM emplace #define EB emplace_back #define BI back_inserter #define MP make_pair #define fst first #define snd second #define DUMP( x ) cerr << #x << " = " << ( x ) << endl constexpr int MOD = 1'000'000'007; // a^x を mod で求める // 反復二乗法 // O( log x ) long long mod_pow( long long a, long long x, long long mod ) { a %= mod; long long res = 1; for ( ; x; x >>= 1, ( a *= a ) %= mod ) { if ( x & 1 ) { ( res *= a ) %= mod; } } return res; } // p が素数のとき、p を法とする剰余体での逆元を求める // Fermat の小定理を利用 // a^{ p - 1 } \equiv 1 ( mod p ) // a^{ p - 2 } \equiv a^{-1} ( mod p ) // incluide : mod_pow int mod_inverse( long long a, long long p ) { return mod_pow( a, p - 2, p ); } // 素数を法とする剰余体での n! を求める class modFact { private: const int MAX_N, MOD; vector fact; public: modFact( const int n, const int mod ) : MAX_N( n ), MOD( mod ), fact( min( MAX_N + 1, MOD ) ) { fact[0] = 1; for ( int i = 1; i < (int)fact.size(); ++i ) { fact[i] = 1LL * fact[ i - 1 ] * i % MOD; } return; } int operator()( const int n ) { int e; return operator()( n, e ); } int operator()( const int n, int &e ) { e = 0; if ( n == 0 ) { return 1; } const long long res = operator()( n / MOD, e ); e += n / MOD; if ( n / MOD % 2 != 0 ) { return res * ( MOD - fact[ n % MOD ] ) % MOD; } return res * fact[ n % MOD ] % MOD; } }; // modfact( max_n, mod ) // ()( n ) // ()( n, e ) // nCr // include : modFact, mod_inverse class modComb { private: const int MOD; modFact mod_fact; public: modComb( const int n, const int mod ) : MOD( mod ), mod_fact( n, mod ) {}; int operator()( const int n, const int r ) { if ( n < 0 || r < 0 || n < r ) { return 0; } int e1, e2, e3; long long a1 = mod_fact( n, e1 ), a2 = mod_fact( r, e2 ), a3 = mod_fact( n - r, e3 ); if ( e1 > e2 + e3 ) { return 0; } return a1 * mod_inverse( a2 * a3 % MOD, MOD ) % MOD; } }; // modComb( n, mod ) // ()( n, r ) modComb nCr( 100'000, MOD ); int main() { cin.tie( 0 ); ios::sync_with_stdio( false ); cout << setprecision( 12 ) << fixed; LL N, M; cin >> N >> M; int res = 0; REP( j, M + 1 ) { ( res += LL( j % 2 ? MOD - 1 : 1 ) * nCr( M, j ) % MOD * mod_pow( M - j, N, MOD ) % MOD ) %= MOD; } cout << res << endl; return 0; }