using System; using System.Collections; using System.Collections.Generic; using System.Diagnostics; using System.IO; using System.Linq; using System.Numerics; using System.Text; using System.Text.RegularExpressions; using System.Threading.Tasks; using static System.Math; using MethodImplAttribute = System.Runtime.CompilerServices.MethodImplAttribute; using MethodImplOptions = System.Runtime.CompilerServices.MethodImplOptions; public static class P { public static void Main() { var pk = Console.ReadLine().Split().Select(int.Parse).ToArray(); var p = pk[0]; var k = pk[1]; Matrix matrix = new Matrix(p, p); for (int i = 0; i < p; i++) { for (int j = 0; j < p; j++) { matrix[i, (i + j) % p]++; matrix[i, (i * j) % p]++; } } Matrix iv = new Matrix(p, 1); iv[0, 0] = 1; var res = Power(matrix, k) * iv; Console.WriteLine(res[0, 0]); } static Matrix Power(Matrix n, long m) { Matrix pow = n; Matrix res = new Matrix(n.Height, n.Width); for (int i = 0; i < n.Height; i++) res[i, i] = 1; while (m > 0) { if ((m & 1) == 1) res *= pow; pow *= pow; m >>= 1; } return res; } } class Matrix { public readonly int Height; public readonly int Width; ModInt[] data; [MethodImpl(MethodImplOptions.AggressiveInlining)] public Matrix(int height, int width) { data = new ModInt[height * width]; Height = height; Width = width; } public ModInt this[int i, int j] { [MethodImpl(MethodImplOptions.AggressiveInlining)] get { return data[i * Width + j]; } [MethodImpl(MethodImplOptions.AggressiveInlining)] set { data[i * Width + j] = value; } } [MethodImpl(MethodImplOptions.AggressiveInlining)] public static Matrix Add(Matrix a, Matrix b) { var res = new Matrix(a.Height, a.Width); for (int i = 0; i < a.Height; i++) for (int j = 0; j < a.Width; j++) res[i, j] = a[i, j] + b[i, j]; return res; } [MethodImpl(MethodImplOptions.AggressiveInlining)] public static Matrix Sub(Matrix a, Matrix b) { var res = new Matrix(a.Height, a.Width); for (int i = 0; i < a.Height; i++) for (int j = 0; j < a.Width; j++) res[i, j] = a[i, j] - b[i, j]; return res; } [MethodImpl(MethodImplOptions.AggressiveInlining)] public static Matrix Mul(Matrix a, Matrix b) { var res = new Matrix(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[i, j] += a[i, k] * b[k, j]; return res; } [MethodImpl(MethodImplOptions.AggressiveInlining)] public static Matrix operator +(Matrix a, Matrix b) => Add(a, b); [MethodImpl(MethodImplOptions.AggressiveInlining)] public static Matrix operator -(Matrix a, Matrix b) => Sub(a, b); [MethodImpl(MethodImplOptions.AggressiveInlining)] public static Matrix operator *(Matrix a, Matrix b) => Mul(a, b); } struct ModInt { public const int Mod = 1000000007; const long POSITIVIZER = ((long)Mod) << 31; long Data; public ModInt(long data) { if ((Data = data % Mod) < 0) Data += Mod; } public static implicit operator long(ModInt modInt) => modInt.Data; public static implicit operator ModInt(long val) => new ModInt(val); public static ModInt operator +(ModInt a, int b) => new ModInt() { Data = (a.Data + b + POSITIVIZER) % Mod }; public static ModInt operator +(ModInt a, long b) => new ModInt(a.Data + b); public static ModInt operator +(ModInt a, ModInt b) { long res = a.Data + b.Data; return new ModInt() { Data = res >= Mod ? res - Mod : res }; } public static ModInt operator -(ModInt a, int b) => new ModInt() { Data = (a.Data - b + POSITIVIZER) % Mod }; public static ModInt operator -(ModInt a, long b) => new ModInt(a.Data - b); public static ModInt operator -(ModInt a, ModInt b) { long res = a.Data - b.Data; return new ModInt() { Data = res < 0 ? res + Mod : res }; } public static ModInt operator *(ModInt a, int b) => new ModInt(a.Data * b); public static ModInt operator *(ModInt a, long b) => a * new ModInt(b); public static ModInt operator *(ModInt a, ModInt b) => new ModInt() { Data = a.Data * b.Data % Mod }; public static ModInt operator /(ModInt a, ModInt b) => new ModInt() { Data = a.Data * GetInverse(b) % Mod }; public static bool operator ==(ModInt a, ModInt b) => a.Data == b.Data; public static bool operator !=(ModInt a, ModInt b) => a.Data != b.Data; public override string ToString() => Data.ToString(); public override bool Equals(object obj) => (ModInt)obj == this; public override int GetHashCode() => (int)Data; static long GetInverse(long a) { long div, p = Mod, x1 = 1, y1 = 0, x2 = 0, y2 = 1; while (true) { if (p == 1) return x2 + Mod; div = a / p; x1 -= x2 * div; y1 -= y2 * div; a %= p; if (a == 1) return x1 + Mod; div = p / a; x2 -= x1 * div; y2 -= y1 * div; p %= a; } } }