using System; using System.IO; using System.Linq; using System.Collections; using System.Collections.Generic; using System.Text; using System.Numerics; using System.Threading.Tasks; using System.Text.RegularExpressions; using static System.Math; using Debug = System.Diagnostics.Debug; using LayoutKind = System.Runtime.InteropServices.LayoutKind; using MethodImplOptions = System.Runtime.CompilerServices.MethodImplOptions; using MethodImplAttribute = System.Runtime.CompilerServices.MethodImplAttribute; static class P { static void Main() { //matrix[i,j]:vector[i]の要素が1であればi行目のj要素に乗算が行われ、そこに遷移する var nk = Console.ReadLine().Split().Select(int.Parse).ToArray(); int n = nk[0]; int k = nk[1]; ModMatrix matrix = new ModMatrix(k * k * k, k * k * k); //k=2の時 // a : 01010101 // ab : 00110011 //abc : 00001111 for (int i = 0; i < matrix.Height; i++) { int val = i; int aCount = val % k; val /= k; int abCount = val % k; val /= k; int abcCount = val % k; int newACount, newABCount, newABCCount; //aが追加された時 newACount = (aCount + 1) % k; newABCount = abCount; newABCCount = abcCount; matrix[i, (newABCCount * k + newABCount) * k + newACount] += 1; //bが追加された時 newACount = aCount; newABCount = (abCount + aCount) % k; newABCCount = abcCount; matrix[i, (newABCCount * k + newABCount) * k + newACount] += 1; //cが追加された時 newACount = aCount; newABCount = abCount; newABCCount = (abcCount + abCount) % k; matrix[i, (newABCCount * k + newABCount) * k + newACount] += 1; } ModMatrix res = new ModMatrix(1, k * k * k); res[0, 0] = 1; long pow = n; while (n > 0) { if ((n & 1) == 1) res *= matrix; matrix *= matrix; n >>= 1; } long resSum = 0; for (int i = 0; i < k * k; i++) resSum += res[0, i]; Console.WriteLine(resSum % 1000000007); } } class ModMatrix : IEquatable { const int MOD = 1000000007; public readonly int Height; public readonly int Width; long[,] data; [MethodImpl(MethodImplOptions.AggressiveInlining)] public ModMatrix(int height, int width) { data = new long[height, width]; Height = height; Width = width; } public long this[int i, int j] { [MethodImpl(MethodImplOptions.AggressiveInlining)] get { return data[i, j]; } [MethodImpl(MethodImplOptions.AggressiveInlining)] set { if ((data[i, j] = value % MOD) < 0) data[i, j] += MOD; } } [MethodImpl(MethodImplOptions.AggressiveInlining)] public bool Equals(ModMatrix other) { if (this.Width != other.Width || this.Height != other.Height) return false; for (int i = 0; i < Height; i++) for (int j = 0; j < Width; j++) if (this[i, j] != other[i, j]) return false; return true; } [MethodImpl(MethodImplOptions.AggressiveInlining)] public static ModMatrix Add(ModMatrix a, ModMatrix b) { Debug.Assert(a.Width == b.Width && a.Height == b.Height); var res = new ModMatrix(a.Height, a.Width); for (int i = 0; i < a.Height; i++) for (int j = 0; j < a.Width; j++) if (MOD <= (res.data[i, j] = a[i, j] + b[i, j])) res.data[i, j] -= MOD; return res; } [MethodImpl(MethodImplOptions.AggressiveInlining)] public static ModMatrix Sub(ModMatrix a, ModMatrix b) { Debug.Assert(a.Width == b.Width && a.Height == b.Height); var res = new ModMatrix(a.Height, a.Width); for (int i = 0; i < a.Height; i++) for (int j = 0; j < a.Width; j++) if ((res.data[i, j] = a[i, j] - b[i, j]) < 0) res.data[i, j] += MOD; return res; } [MethodImpl(MethodImplOptions.AggressiveInlining)] public static ModMatrix Mul(ModMatrix a, ModMatrix b) { Debug.Assert(a.Width == b.Height); var res = new ModMatrix(a.Height, b.Width); for (int i = 0; i < a.Height; i++) for (int j = 0; j < b.Width; j++) { for (int k = 0; k < a.Width; k++) res.data[i, j] += a[i, k] * b[k, j] % MOD; res.data[i, j] %= MOD; } return res; } [MethodImpl(MethodImplOptions.AggressiveInlining)] public static ModMatrix operator +(ModMatrix a, ModMatrix b) => Add(a, b); [MethodImpl(MethodImplOptions.AggressiveInlining)] public static ModMatrix operator -(ModMatrix a, ModMatrix b) => Sub(a, b); [MethodImpl(MethodImplOptions.AggressiveInlining)] public static ModMatrix operator *(ModMatrix a, ModMatrix b) => Mul(a, b); [MethodImpl(MethodImplOptions.AggressiveInlining)] public static bool operator ==(ModMatrix a, ModMatrix b) => a.Equals(b); [MethodImpl(MethodImplOptions.AggressiveInlining)] public static bool operator !=(ModMatrix a, ModMatrix b) => !a.Equals(b); }