using System.Diagnostics; using System; using System.Linq; using System.Numerics; using System.Collections; using System.Collections.Generic; using System.IO; using System.Text; using static Functions; using N = System.Int64; static class Program { static public void Main(string[] args) { Console.SetOut(new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false }); var solver = new Solver(); solver.Solve(); Console.Out.Flush(); } } public class Solver { public void Solve() { int n = ri, m = ri; var pown = new ModInt[n + m + 1]; var powm = new ModInt[n + m + 1]; for (int i = 0; i < n + m + 1; i++) { pown[i] = new ModInt(i).Pow(n); powm[i] = new ModInt(i).Pow(m); } var f = new ModFrac(n + m + 1); var s = new ModInt[n + m + 1]; for (int k = 1; k <= n + m; k++) { for (int l = 0; l <= k; l++) s[k] += f.fi[l] * f.fi[k - l] * pown[k - l] * powm[l]; if ((k & 1) == 1) s[k] = -s[k]; } var a = new ModInt[n + m + 1]; for (int t = 2; t < n + m + 1; t++) { for (int k = 1; k <= t; k++) a[t] += s[k] * f.fi[t - k]; a[t] *= f.f[t]; if ((t & 1) == 1) a[t] = -a[t]; } Write(Interpolate(a, new ModInt(5) / 2)); } struct ModInt { private const long _mod = 1000000007; //private const long _mod = 998244353; long Val; public ModInt(long v) { Val = v; } public override string ToString() { return Val.ToString(); } public override bool Equals(object obj) => obj is ModInt other && this.Equals(other); public bool Equals(ModInt x) => Val == x.Val; public override int GetHashCode() => Val.GetHashCode(); public static bool operator ==(ModInt a, ModInt b) { return a.Val == b.Val; } public static bool operator !=(ModInt a, ModInt b) { return a.Val != b.Val; } public static implicit operator ModInt(long n) { long r = n % _mod; return new ModInt(r < 0 ? r + _mod : r); } public static ModInt operator +(ModInt a, ModInt b) { long r = a.Val + b.Val; return new ModInt(r < _mod ? r : r - _mod); } public static ModInt operator -(ModInt a, ModInt b) { long r = a.Val - b.Val; return new ModInt(r < 0 ? r + _mod : r); } public static ModInt operator -(ModInt a) => new ModInt(a.Val == 0 ? 0 : _mod - a.Val); public static ModInt operator *(ModInt a, ModInt b) => new ModInt(a.Val * b.Val % _mod); public static ModInt operator /(ModInt a, ModInt b) => a * b.Inv; public ModInt Pow(long n) { long t = Val, r = 1; while (n > 0) { if ((n & 1) == 1) r = r * t % _mod; t = t * t % _mod; n >>= 1; } return new ModInt(r); } public ModInt Inv { get { return this.Pow(_mod - 2); } } } ModInt Interpolate(in ModInt[] a, ModInt x) // f(0),...,f(n-1) { int n = a.Length - 1; var f = new ModFrac(n); var s = new ModInt(n % 2 == 0 ? 1 : -1); ModInt g = 1; for (int i = 0; i <= n; i++) g *= x - i; ModInt ret = 0; for (int i = 0; i <= n; i++) { ModInt c = s * a[i] * f.fi[i] * f.fi[n - i]; s *= -1; if (x == i) { ModInt p = 1; for (int j = 0; j < i; j++) p *= x - j; for (int j = i + 1; j <= n; j++) p *= x - j; ret += c * p; } else ret += c * g / (x - i); } return ret; } class ModFrac { public ModInt[] f; public ModInt[] fi; public ModFrac(long n) { f = new ModInt[n + 1]; fi = new ModInt[n + 1]; f[0] = 1; for (long i = 0; i < n; i++) f[i + 1] = f[i] * (i + 1); fi[n] = f[n].Inv; for (long i = n; i > 0; i--) fi[i - 1] = fi[i] * i; } public ModInt Binom(long n, long k) { if (n < 0) return 0; if (n == 0) return k == 0 ? 1 : 0; return 0 <= k && k <= n ? f[n] * fi[k] * fi[n - k] : 0; } } const long inf = (long)1 << 60; int ri { get { return (int)sc.Integer(); } } long rl { get { return sc.Integer(); } } double rd { get { return sc.Double(); } } string rs { get { return sc.Scan(); } } string rline { get { return sc.Line(); } } public StreamScanner sc = new StreamScanner(Console.OpenStandardInput()); T[] RepArray(T t, int count) => Enumerable.Repeat(t, count).ToArray(); void WriteJoin(string s, IEnumerable t) { Console.WriteLine(string.Join(s, t)); } void WriteMax(params long[] x) => Console.Write(x.Max()); void WriteMin(params long[] x) => Console.Write(x.Min()); void Write(T t) { Console.WriteLine(t.ToString()); } void WriteFlush(T t) { Console.WriteLine(t.ToString()); Console.Out.Flush(); } void WriteError(T t) { Console.Error.WriteLine(t.ToString()); } void YN(bool t) { Console.WriteLine(t ? "YES" : "NO"); } void Yn(bool t) { Console.WriteLine(t ? "Yes" : "No"); } void yn(bool t) { Console.WriteLine(t ? "yes" : "no"); } } public static class Functions { public static int Popcount(long x) { x = x - ((x >> 1) & 0x5555555555555555); x = (x & 0x3333333333333333) + ((x >> 2) & 0x3333333333333333); x = (x + (x >> 4)) & 0x0f0f0f0f0f0f0f0f; x = x + (x >> 8); x = x + (x >> 16); x = x + (x >> 32); return (int)(x & 0x0000007f); } public static int Ctz(long x) { if (x == 0) return -1; return Popcount((x & -x) - 1); } public static int SafeMod(int x, int m) { int r = x % m; return r < 0 ? r + m : r; } public static long SafeMod(long x, long m) { long r = x % m; return r < 0 ? r + m : r; } public static long Floor(long a, long b) => a >= 0 ? a / b : (a + 1) / b - 1; public static long Ceil(long a, long b) => a > 0 ? (a - 1) / b + 1 : a / b; public static int Gcd(int a, int b) => b == 0 ? a : Gcd(b, a % b); public static long Gcd(long a, long b) => b == 0 ? a : Gcd(b, a % b); public static void Swap(ref int x, ref int y) { x ^= y; y ^= x; x ^= y; } public static void Swap(ref long x, ref long y) { x ^= y; y ^= x; x ^= y; } public static void Swap(ref T x, ref T y) { T t = y; y = x; x = t; } public static T Clamp(T x, T l, T r) where T : IComparable => x.CompareTo(l) <= 0 ? l : (x.CompareTo(r) <= 0 ? x : r); public static void Chmin(ref T x, T y) where T : IComparable { if (x.CompareTo(y) > 0) x = y; } public static void Chmax(ref T x, T y) where T : IComparable { if (x.CompareTo(y) < 0) x = y; } public static int LowerBound(in T[] list, S val, Func comp) { if (list.Length == 0) return -1; int l = 0, r = list.Length; while (l < r) { int x = (l + r) / 2; if (comp(list[x], val) < 0) l = x + 1; else r = x; } return l; } public static int LowerBound(in List list, S val, Func comp) { if (list.Count == 0) return -1; int l = 0, r = list.Count; while (l < r) { int x = (l + r) / 2; if (comp(list[x], val) < 0) l = x + 1; else r = x; } return l; } public static int UpperBound(in List list, S val, Func comp) { if (list.Count == 0) return 0; if (comp(list.Last(), val) < 0) return list.Count; int l = 0, r = list.Count; while (l < r) { int x = (l + r) / 2; if (comp(list[x], val) <= 0) l = x + 1; else r = x; } return l; } } public class StreamScanner { public StreamScanner(Stream stream) { str = stream; } private readonly Stream str; private readonly byte[] buf = new byte[1024]; private int len, ptr; public bool isEof = false; public bool IsEndOfStream { get { return isEof; } } private byte read() { if (isEof) throw new EndOfStreamException(); if (ptr >= len) { ptr = 0; if ((len = str.Read(buf, 0, 1024)) <= 0) { isEof = true; return 0; } } return buf[ptr++]; } public char Char() { byte b = 0; do b = read(); while (b < 33 || 126 < b); return (char)b; } public string Line() { var sb = new StringBuilder(); for (var b = Char(); b != 10 && !isEof; b = (char)read()) sb.Append(b); return sb.ToString(); } public string Scan() { var sb = new StringBuilder(); for (var b = Char(); b >= 33 && b <= 126; b = (char)read()) sb.Append(b); return sb.ToString(); } public long Integer() { long ret = 0; byte b = 0; var ng = false; do b = read(); while (b != '-' && (b < '0' || '9' < b)); if (b == '-') { ng = true; b = read(); } for (; true; b = read()) { if (b < '0' || '9' < b) return ng ? -ret : ret; else ret = ret * 10 + b - '0'; } } public double Double() { return double.Parse(Scan()); } }