using System; using System.Collections.Generic; using System.Linq; using System.IO; using System.Runtime.CompilerServices; using System.Text; using System.Diagnostics; using System.Numerics; using static System.Console; using static System.Convert; using static System.Math; using static Template; using Pi = Pair; class Solver { public void Solve(Scanner sc) { int N, M; sc.Make(out N, out M); ModInt.Build(201010); ModInt res = 0; for(int i = 0; i <= M; i++) { if ((M - i) % 2 == 0) res += ModInt.Comb(M, i) * ModInt.Pow(i, N); else res-= ModInt.Comb(M, i) * ModInt.Pow(i, N); } WriteLine(res); } } public struct ModInt { public const long MOD = (int)1e9 + 7; //public const long MOD = 998244353; public long Value { get; set; } public ModInt(long n = 0) { Value = n; } private static ModInt[] fac;//ιšŽδΉ— private static ModInt[] inv;//逆数 private static ModInt[] facinv;//1/(i!) public override string ToString() => Value.ToString(); [MethodImpl(MethodImplOptions.AggressiveInlining)] public static ModInt operator +(ModInt l, ModInt r) { l.Value += r.Value; if (l.Value >= MOD) l.Value -= MOD; return l; } [MethodImpl(MethodImplOptions.AggressiveInlining)] public static ModInt operator -(ModInt l, ModInt r) { l.Value -= r.Value; if (l.Value < 0) l.Value += MOD; return l; } [MethodImpl(MethodImplOptions.AggressiveInlining)] public static ModInt operator *(ModInt l, ModInt r) => new ModInt(l.Value * r.Value % MOD); [MethodImpl(MethodImplOptions.AggressiveInlining)] public static ModInt operator /(ModInt l, ModInt r) => l * Pow(r, MOD - 2); [MethodImpl(MethodImplOptions.AggressiveInlining)] public static implicit operator long(ModInt l) => l.Value; [MethodImpl(MethodImplOptions.AggressiveInlining)] public static implicit operator ModInt(long n) { n %= MOD; if (n < 0) n += MOD; return new ModInt(n); } public static ModInt Pow(ModInt m, long n) { if (n == 0) return 1; if (n % 2 == 0) return Pow(m * m, n >> 1); else return Pow(m * m, n >> 1) * m; } public static void Build(int n) { fac = new ModInt[n + 1]; facinv = new ModInt[n + 1]; inv = new ModInt[n + 1]; inv[1] = 1; fac[0] = fac[1] = 1; facinv[0] = facinv[1] = 1; for (var i = 2; i <= n; i++) { fac[i] = fac[i - 1] * i; inv[i] = MOD - inv[MOD % i] * (MOD / i); facinv[i] = facinv[i - 1] * inv[i]; } } [MethodImpl(MethodImplOptions.AggressiveInlining)] public static ModInt Fac(ModInt n) => fac[n]; [MethodImpl(MethodImplOptions.AggressiveInlining)] public static ModInt Inv(ModInt n) => inv[n]; [MethodImpl(MethodImplOptions.AggressiveInlining)] public static ModInt FacInv(ModInt n) => facinv[n]; [MethodImpl(MethodImplOptions.AggressiveInlining)] public static ModInt Comb(ModInt n, ModInt r) { if (n < r) return 0; if (n == r) return 1; var calc = fac[n]; calc = calc * facinv[r]; calc = calc * facinv[n - r]; return calc; } } #region Template public static class Template { static void Main(string[] args) { Console.SetOut(new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false }); new Solver().Solve(new Scanner()); Console.Out.Flush(); } [MethodImpl(MethodImplOptions.AggressiveInlining)] public static bool chmin(ref T a, T b) where T : IComparable { if (a.CompareTo(b) == 1) { a = b; return true; } return false; } [MethodImpl(MethodImplOptions.AggressiveInlining)] public static bool chmax(ref T a, T b) where T : IComparable { if (a.CompareTo(b) == -1) { a = b; return true; } return false; } [MethodImpl(MethodImplOptions.AggressiveInlining)] public static void swap(ref T a, ref T b) { var t = b; b = a; a = t; } [MethodImpl(MethodImplOptions.AggressiveInlining)] public static void swap(this IList A, int i, int j) { var t = A[i]; A[i] = A[j]; A[j] = t; } public static T[] Create(int n, Func f) { var rt = new T[n]; for (var i = 0; i < rt.Length; ++i) rt[i] = f(); return rt; } public static T[] Create(int n, Func f) { var rt = new T[n]; for (var i = 0; i < rt.Length; ++i) rt[i] = f(i); return rt; } public static IEnumerable Shuffle(this IEnumerable A) => A.OrderBy(v => Guid.NewGuid()); public static int CompareTo(this T[] A, T[] B, Comparison cmp = null) { cmp = cmp ?? Comparer.Default.Compare; for (var i = 0; i < Min(A.Length, B.Length); i++) { int c = cmp(A[i], B[i]); if (c > 0) return 1; else if (c < 0) return -1; } if (A.Length == B.Length) return 0; if (A.Length > B.Length) return 1; else return -1; } public static int MaxElement(this IList A, Comparison cmp = null) { cmp = cmp ?? Comparer.Default.Compare; T max = A[0]; int rt = 0; for (int i = 1; i < A.Count; i++) if (cmp(max, A[i]) < 0) { max = A[i]; rt = i; } return rt; } public static T PopBack(this List A){ var v = A[A.Count - 1]; A.RemoveAt(A.Count - 1);return v; } public static void Fail(T s) { Console.WriteLine(s); Console.Out.Close(); Environment.Exit(0); } } public class Scanner { public string Str => Console.ReadLine().Trim(); public int Int => int.Parse(Str); public long Long => long.Parse(Str); public double Double => double.Parse(Str); public int[] ArrInt => Str.Split(' ').Select(int.Parse).ToArray(); public long[] ArrLong => Str.Split(' ').Select(long.Parse).ToArray(); public char[][] Grid(int n) => Create(n, () => Str.ToCharArray()); public int[] ArrInt1D(int n) => Create(n, () => Int); public long[] ArrLong1D(int n) => Create(n, () => Long); public int[][] ArrInt2D(int n) => Create(n, () => ArrInt); public long[][] ArrLong2D(int n) => Create(n, () => ArrLong); private Queue q = new Queue(); [MethodImpl(MethodImplOptions.AggressiveInlining)] public T Next() { if (q.Count == 0) foreach (var item in Str.Split(' ')) q.Enqueue(item); return (T)Convert.ChangeType(q.Dequeue(), typeof(T)); } public void Make(out T1 v1) => v1 = Next(); public void Make(out T1 v1, out T2 v2) { v1 = Next(); v2 = Next(); } public void Make(out T1 v1, out T2 v2, out T3 v3) { Make(out v1, out v2); v3 = Next(); } public void Make(out T1 v1, out T2 v2, out T3 v3, out T4 v4) { Make(out v1, out v2, out v3); v4 = Next(); } public void Make(out T1 v1, out T2 v2, out T3 v3, out T4 v4, out T5 v5) { Make(out v1, out v2, out v3, out v4); v5 = Next(); } public void Make(out T1 v1, out T2 v2, out T3 v3, out T4 v4, out T5 v5, out T6 v6) { Make(out v1, out v2, out v3, out v4, out v5); v6 = Next(); } //public (T1, T2) Make() { Make(out T1 v1, out T2 v2); return (v1, v2); } //public (T1, T2, T3) Make() { Make(out T1 v1, out T2 v2, out T3 v3); return (v1, v2, v3); } //public (T1, T2, T3, T4) Make() { Make(out T1 v1, out T2 v2, out T3 v3, out T4 v4); return (v1, v2, v3, v4); } } public class Pair : IComparable> { public T1 v1; public T2 v2; public Pair() { } public Pair(T1 v1, T2 v2) { this.v1 = v1; this.v2 = v2; } [MethodImpl(MethodImplOptions.AggressiveInlining)] public int CompareTo(Pair p) { var c = Comparer.Default.Compare(v1, p.v1); if (c == 0) c = Comparer.Default.Compare(v2, p.v2); return c; } public override string ToString() => $"{v1.ToString()} {v2.ToString()}"; public void Deconstruct(out T1 a, out T2 b) { a = v1; b = v2; } } public class Pair : Pair, IComparable> { public T3 v3; public Pair() : base() { } public Pair(T1 v1, T2 v2, T3 v3) : base(v1, v2) { this.v3 = v3; } [MethodImpl(MethodImplOptions.AggressiveInlining)] public int CompareTo(Pair p) { var c = base.CompareTo(p); if (c == 0) c = Comparer.Default.Compare(v3, p.v3); return c; } public override string ToString() => $"{base.ToString()} {v3.ToString()}"; public void Deconstruct(out T1 a, out T2 b, out T3 c) { Deconstruct(out a, out b); c = v3; } } #endregion