using System; using System.Collections.Generic; using System.Linq; using System.Linq.Expressions; using System.IO; using System.Text; using System.Diagnostics; using static util; using P = pair; using Binary = System.Func; using Unary = System.Func; class Program { static StreamWriter sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false }; static Scan sc = new Scan(); const int M = 1000000007; const double eps = 1e-11; static readonly int[] dd = { 0, 1, 0, -1, 0 }; static void Main() { long n, m; sc.Multi(out n, out m); var tmp = m; long min = M; for (long i = 2; i * i <= m; i++) { if (m % i == 0) { int c = 0; while (m % i == 0) { ++c; m /= i; } long cc = 0; long a = i; while (a <= n) { cc += n / a; a *= i; } min = Math.Min(min, cc / c); } } if (m > 1) { long cc = 0; long a = m; while (a <= n) { cc += n / a; a *= m; } min = Math.Min(min, cc); } Prt(getperm(n) / BigDouble.pow(tmp, min)); sw.Flush(); } struct BigDouble { public double man; public long exp; void normalize() { while (man >= 10) { man /= 10; ++exp; } while (man < 1) { man *= 10; --exp; } } public BigDouble(double a) : this(a, 0) {} public BigDouble(double a, long b){ man = a; exp = b; normalize(); } public static implicit operator BigDouble(double a) => new BigDouble(a); public static BigDouble operator*(BigDouble a, BigDouble b) { return new BigDouble(a.man * b.man, a.exp + b.exp); } public static BigDouble operator/(BigDouble a, BigDouble b) { return new BigDouble(a.man / b.man, a.exp - b.exp); } public static BigDouble operator+(BigDouble a, BigDouble b) { if (a.exp >= b.exp) return new BigDouble(a.man + b.man * Math.Pow(10, b.exp - a.exp), a.exp); else return new BigDouble(a.man * Math.Pow(10, a.exp - b.exp) + b.man, b.exp); } public static BigDouble pow(BigDouble a, long k) { if (k == 0) return 1; var t = pow(a, k / 2); if ((k & 1) == 0) return t * t; return t * t * a; } // a ^ (10^k) = (a^10)^(10^(k - 1)) public static BigDouble pow10k(BigDouble a, long k) { if (k == 0) return a; return pow10k(new BigDouble(Math.Pow(a.man, 10), a.exp * 10), k - 1); } public override string ToString() { return man + "e" + exp; } } static BigDouble getperm(long n) { BigDouble ret = 1; if (n < 10000) { for (int i = 2; i <= n; i++) ret *= i; return ret; } return Math.Sqrt(Math.PI * 2 * n) * BigDouble.pow(n / Math.E, n) * (1 + 1 / (12.0 * n) + 1 / (288.0 * n * n) - 139 / (51840.0 * n * n * n)); // ret = n + 109535241009.0 / 48264275462.0; // ret = n + 29944523.0 / 19733142.0 / ret; // ret = n + 22999.0 / 22737.0 / ret; // ret = n + 195.0 / 371.0 / ret; // ret = n + 53.0 / 210.0 / ret; // ret = n + 1 / 30.0 / ret; // ret = 1 / 12.0 / ret; // ret += Math.Log(Math.PI * 2) / 2 - n + (n + 0.5) * Math.Log(n); // return BigDouble.pow10k(Math.Exp(ret.man), ret.exp); } static void DBG(string a) { Console.WriteLine(a); } static void DBG(IEnumerable a) { DBG(string.Join(" ", a)); } static void DBG(params object[] a) { DBG(string.Join(" ", a)); } static void Prt(string a) { sw.WriteLine(a); } static void Prt(IEnumerable a) { Prt(string.Join(" ", a)); } static void Prt(params object[] a) { Prt(string.Join(" ", a)); } // for AOJ // static string Join(string sep, IEnumerable a) { return string.Join(sep, a.Select(x => x.ToString()).ToArray()); } // static void DBG(IEnumerable a) { DBG(Join(" ", a)); } // static void DBG(params object[] a) { DBG(Join(" ", a)); } // static void Prt(IEnumerable a) { Prt(Join(" ", a)); } // static void Prt(params object[] a) { Prt(Join(" ", a)); } } class pair : IComparable> where T : IComparable where U : IComparable { public T v1; public U v2; public pair(T v1, U v2) { this.v1 = v1; this.v2 = v2; } public int CompareTo(pair a) { return v1.CompareTo(a.v1) != 0 ? v1.CompareTo(a.v1) : v2.CompareTo(a.v2); } public override string ToString() { return v1 + " " + v2; } } static class util { public static pair make_pair(T v1, U v2) where T : IComparable where U : IComparable { return new pair(v1, v2); } public static T Max(params T[] a) { return a.Max(); } public static T Min(params T[] a) { return a.Min(); } public static void swap(ref T a, ref T b) { var t = a; a = b; b = t; } 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[] copy(this IList a) { var ret = new T[a.Count]; for (int i = 0; i < a.Count; i++) ret[i] = a[i]; return ret; } } static class Operator { static readonly ParameterExpression x = Expression.Parameter(typeof(T), "x"); static readonly ParameterExpression y = Expression.Parameter(typeof(T), "y"); public static readonly Func Add = Lambda(Expression.Add); public static readonly Func Subtract = Lambda(Expression.Subtract); public static readonly Func Multiply = Lambda(Expression.Multiply); public static readonly Func Divide = Lambda(Expression.Divide); public static readonly Func Plus = Lambda(Expression.UnaryPlus); public static readonly Func Negate = Lambda(Expression.Negate); public static Func Lambda(Binary op) { return Expression.Lambda>(op(x, y), x, y).Compile(); } public static Func Lambda(Unary op) { return Expression.Lambda>(op(x), x).Compile(); } } class Scan { public int Int { get { return int.Parse(Str); } } public long Long { get { return long.Parse(Str); } } public double Double { get { return double.Parse(Str); } } public string Str { get { return Console.ReadLine().Trim(); } } public int[] IntArr { get { return StrArr.Select(int.Parse).ToArray(); } } public long[] LongArr { get { return StrArr.Select(long.Parse).ToArray(); } } public double[] DoubleArr { get { return StrArr.Select(double.Parse).ToArray(); } } public string[] StrArr { get { return Str.Split(); } } bool eq() { return typeof(T).Equals(typeof(U)); } T ct(U a) { return (T)Convert.ChangeType(a, typeof(T)); } T cv(string s) { return eq() ? ct(int.Parse(s)) : eq() ? ct(long.Parse(s)) : eq() ? ct(double.Parse(s)) : eq() ? ct(s[0]) : ct(s); } public void Multi(out T a) { a = cv(Str); } public void Multi(out T a, out U b) { var ar = StrArr; a = cv(ar[0]); b = cv(ar[1]); } public void Multi(out T a, out U b, out V c) { var ar = StrArr; a = cv(ar[0]); b = cv(ar[1]); c = cv(ar[2]); } public void Multi(out T a, out U b, out V c, out W d) { var ar = StrArr; a = cv(ar[0]); b = cv(ar[1]); c = cv(ar[2]); d = cv(ar[3]); } public void Multi(out T a, out U b, out V c, out W d, out X e) { var ar = StrArr; a = cv(ar[0]); b = cv(ar[1]); c = cv(ar[2]); d = cv(ar[3]); e = cv(ar[4]); } public void Multi(out T a, out U b, out V c, out W d, out X e, out Y f) { var ar = StrArr; a = cv(ar[0]); b = cv(ar[1]); c = cv(ar[2]); d = cv(ar[3]); e = cv(ar[4]); f = cv(ar[5]); } public void Multi(out T a, out U b, out V c, out W d, out X e, out Y f, out Z g) { var ar = StrArr; a = cv(ar[0]); b = cv(ar[1]); c = cv(ar[2]); d = cv(ar[3]); e = cv(ar[4]); f = cv(ar[5]); g = cv(ar[6]);} } static class mymath { public static long Mod = 1000000007; public static bool isprime(long a) { if (a < 2) return false; for (long i = 2; i * i <= a; i++) if (a % i == 0) return false; return true; } public static bool[] sieve(int n) { var p = new bool[n + 1]; for (int i = 2; i <= n; i++) p[i] = true; for (int i = 2; i * i <= n; i++) if (p[i]) for (int j = i * i; j <= n; j += i) p[j] = false; return p; } public static List getprimes(int n) { var prs = new List(); var p = sieve(n); for (int i = 2; i <= n; i++) if (p[i]) prs.Add(i); return prs; } public static long[][] E(int n) { var ret = new long[n][]; for (int i = 0; i < n; i++) { ret[i] = new long[n]; ret[i][i] = 1; } return ret; } public static double[][] dE(int n) { var ret = new double[n][]; for (int i = 0; i < n; i++) { ret[i] = new double[n]; ret[i][i] = 1; } return ret; } public static long[][] pow(long[][] A, long n) { if (n == 0) return E(A.Length); var t = pow(A, n / 2); if ((n & 1) == 0) return mul(t, t); return mul(mul(t, t), A); } public static double[][] pow(double[][] A, long n) { if (n == 0) return dE(A.Length); var t = pow(A, n / 2); if ((n & 1) == 0) return mul(t, t); return mul(mul(t, t), A); } public static double dot(double[] x, double[] y) { int n = x.Length; double ret = 0; for (int i = 0; i < n; i++) ret += x[i] * y[i]; return ret; } public static double _dot(double[] x, double[] y) { int n = x.Length; double ret = 0, r = 0; for (int i = 0; i < n; i++) { double s = ret + (x[i] * y[i] + r); r = (x[i] * y[i] + r) - (s - ret); ret = s; } return ret; } public static long dot(long[] x, long[] y) { int n = x.Length; long ret = 0; for (int i = 0; i < n; i++) ret = (ret + x[i] * y[i]) % Mod; return ret; } public static T[][] trans(T[][] A) { int n = A[0].Length, m = A.Length; var ret = new T[n][]; for (int i = 0; i < n; i++) { ret[i] = new T[m]; for (int j = 0; j < m; j++) ret[i][j] = A[j][i]; } return ret; } public static double[] mul(double[][] A, double[] x) { int n = A.Length; var ret = new double[n]; for (int i = 0; i < n; i++) ret[i] = dot(x, A[i]); return ret; } public static long[] mul(long[][] A, long[] x) { int n = A.Length; var ret = new long[n]; for (int i = 0; i < n; i++) ret[i] = dot(x, A[i]); return ret; } public static long[][] mul(long[][] A, long[][] B) { int n = A.Length; var Bt = trans(B); var ret = new long[n][]; for (int i = 0; i < n; i++) ret[i] = mul(Bt, A[i]); return ret; } public static double[][] mul(double[][] A, double[][] B) { int n = A.Length; var Bt = trans(B); var ret = new double[n][]; for (int i = 0; i < n; i++) ret[i] = mul(Bt, A[i]); return ret; } public static long[] add(long[] x, long[] y) { int n = x.Length; var ret = new long[n]; for (int i = 0; i < n; i++) ret[i] = (x[i] + y[i]) % Mod; return ret; } public static long[][] add(long[][] A, long[][] B) { int n = A.Length; var ret = new long[n][]; for (int i = 0; i < n; i++) ret[i] = add(A[i], B[i]); return ret; } public static long pow(long a, long b) { if (a >= Mod) return pow(a % Mod, b); if (a == 0) return 0; if (b == 0) return 1; var t = pow(a, b / 2); if ((b & 1) == 0) return t * t % Mod; return t * t % Mod * a % Mod; } public static long inv(long a) { return pow(a, Mod - 2); } public static long gcd(long a, long b) { while (b > 0) { var t = a % b; a = b; b = t; } return a; } // a x + b y = gcd(a, b) public static long extgcd(long a, long b, out long x, out long y) { long g = a; x = 1; y = 0; if (b > 0) { g = extgcd(b, a % b, out y, out x); y -= a / b * x; } return g; } public static long lcm(long a, long b) { return a / gcd(a, b) * b; } static long[] facts; public static long[] setfacts(int n) { facts = new long[n + 1]; facts[0] = 1; for (int i = 0; i < n; i++) facts[i + 1] = facts[i] * (i + 1) % Mod; return facts; } public static long comb(int n, int r) { if (n < 0 || r < 0 || r > n) return 0; if (n - r < r) r = n - r; if (r == 0) return 1; if (r == 1) return n; if (facts != null && facts.Length > n) return facts[n] * inv(facts[r]) % Mod * inv(facts[n - r]) % Mod; int[] numer = new int[r], denom = new int[r]; for (int k = 0; k < r; k++) { numer[k] = n - r + k + 1; denom[k] = k + 1; } for (int p = 2; p <= r; p++) { int piv = denom[p - 1]; if (piv > 1) { int ofst = (n - r) % p; for (int k = p - 1; k < r; k += p) { numer[k - ofst] /= piv; denom[k] /= piv; } } } long ret = 1; for (int k = 0; k < r; k++) if (numer[k] > 1) ret = ret * numer[k] % Mod; return ret; } public static long[][] getcombs(int n) { var ret = new long[n + 1][]; for (int i = 0; i <= n; i++) { ret[i] = new long[i + 1]; ret[i][0] = ret[i][i] = 1; for (int j = 1; j < i; j++) ret[i][j] = (ret[i - 1][j - 1] + ret[i - 1][j]) % Mod; } return ret; } // nC0, nC2, ..., nCn public static long[] getcomb(int n) { var ret = new long[n + 1]; ret[0] = 1; for (int i = 0; i < n; i++) ret[i + 1] = ret[i] * (n - i) % Mod * inv(i + 1) % Mod; return ret; } }