Problem:
Score : 300 points

Problem Statement

There are N integers a_1, a_2, ..., a_N not less than 1.
The values of a_1, a_2, ..., a_N are not known, but it is known that a_1 \times a_2 \times ... \times a_N = P.

Find the maximum possible greatest common divisor of a_1, a_2, ..., a_N.

Constraints

1 \leq N \leq 10^{12}

1 \leq P \leq 10^{12}

Input

Input is given from Standard Input in the following format:

N P

Output

Print the answer.

Sample Input 1

3 24

Sample Output 1

2

The greatest common divisor would be 2 when, for example, a_1=2, a_2=6 and a_3=2.

Sample Input 2

5 1

Sample Output 2

1

As a_i are positive integers, the only possible case is a_1 = a_2 = a_3 = a_4 = a_5 = 1.

Sample Input 3

1 111

Sample Output 3

111

Sample Input 4

4 972439611840

Sample Output 4

206

Solution in C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections;
using System.Collections.Generic;
using System.Linq;
using System.Diagnostics;
using System.Text;
using System.Text.RegularExpressions;
using System.Threading.Tasks;
using System.Numerics;
using System.IO;
using System.Runtime.InteropServices;
using static System.Math;
using static Math2;
using static io;
using static Utils;

public class CompetitiveProgramming
{
  public void Solve()
  {
    var o = Longs;
    var N = o[0];
    var P = o[1];
    long ans = 1;
    var a = NumberTheory.PrimeFactorization(P);
    foreach (var i in a)
    {
      var y = i.Value / N;
      ans *= Power2(i.Key, y);

    }
    Write(ans);
  }
}

public static class NumberTheory
{
  public static Dictionary<long, int> PrimeFactorization(long N)
  {
    var ret = new Dictionary<long, int>();
    for (long i = 2; i * i <= N; ++i)
    {
      int cnt = 0;
      while (N % i == 0)
      {
        cnt++;
        N /= i;
      }
      if (cnt != 0) ret[i] = cnt;
    }
    if (N >= 2) ret[N] = 1;
    return ret;
  }
  public static List<long> DivisorEnumrate(long N)
  {
    var ret = new List<long>();
    for (long i = 1; i * i <= N; ++i)
    {
      if (N % i == 0)
      {
        ret.Add(i);
        ret.Add(N / i);
      }
    }
    return ret;
  }

}

public static class Math2
{
  public const int INF = 1 << 29;
  public const long INFL = 1L << 60;
  public const int MOD = 1000000007;
  public const int MOD2 = 998244353;

  public static long Power(long i, long N, long MOD = 1000000007)//i^N
  {
    long res = 1;
    while (N > 0)
    {
      if ((N & 1) != 0) res = res * i % MOD;
      i = i * i % MOD;
      N >>= 1;
    }
    return res;
  }
  public static long Power2(long i, long N)//i^N
  {
    long res = 1;
    while (N > 0)
    {
      if ((N & 1) != 0) res = res * i;
      i = i * i;
      N >>= 1;
    }
    return res;
  }
  public static long GCD(long i, long N)
  {
    if (i > N) Swap(ref i, ref N);
    if (i == 0) return N;
    while (N != 0)
    {
      var r = i % N;
      i = N;
      N = r;
    }
    return i;
  }
  public static long LCM(long i, long N) => i * N / GCD(i, N);
  public static long Comb(long N, long R, int MOD = 1000000007)
  {
    long ret = 1;
    long x = 1;
    for (long i = N; i >= N - R + 1; --i)
    {
      ret = ret / x * i;
      ret %= MOD;
      x++;
    }
    return ret;
  }
  public static long Comb2(long N, long R)
  {
    long Nume = 1;
    long Deno = 1;

    if (R > N - R) Swap(ref N, ref R);
    for (long i = 1; i <= R; ++i)
    {
      Deno *= i;
      Nume *= N - i + 1;
    }
    return Deno / Nume;
  }

}
public static class Utils
{

  public static void Swap<T>(ref T A, ref T B)
  {
    T x = A;
    A = B;
    B = x;
  }
  public static int DigitSum(int N)
  {
    string s = N.ToString();
    int ret = 0;
    for (int i = 0; i < s.Length; ++i) ret += s[i] - '0';
    return ret;
  }
}
class Program
{
  static void Main(string[] args)
  {
    var CompetitiveProgramming = new CompetitiveProgramming();
    CompetitiveProgramming.Solve();
  }
}
public static class io
{
  public static string Str => Console.ReadLine();
  public static string[] Strs => Str.Split(' ');
  public static long[] Longs => Strs.Select(long.Parse).ToArray();
  public static int[] Ints => Strs.Select(int.Parse).ToArray();
  public static char[] Chars => Str.ToArray();
  public static double[] Doubles => Strs.Select(double.Parse).ToArray();
  public static long Long1 => Longs[0];
  public static int Int1 => Ints[0];
  public static char Char1 => Chars[0];
  public static double Double1 => Doubles[0];
  public static long[] HorizontalRead(int N) { long[] A = new long[N]; for (int i = 0; i < N; ++i) A[i] = Long1; return A; }
  public static void Write(string a) => Console.WriteLine(a);
  public static void Write(params object[] i) => Write(string.Join(" ", i));
  public static void Write<T>(IEnumerable<T> a) => Write(string.Join(" ", a));
  public static void Horizontalwrite<T>(IEnumerable<T> a) { foreach (var z in a) Write(z); }
  public static void YN(bool i) { if (i) Write("Yes"); else Write("No"); }
}