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: Time Limit Exceeded)

using System;
using System.Collections.Generic;
using System.IO;
using System.Runtime.InteropServices;
using System.Security.Cryptography;

namespace Contest
{
    class Scanner
    {
        public Scanner()
        {
            _stream = new StreamReader(Console.OpenStandardInput());
            _pos = 0;
            _line = new string[0];
            _separator = ' ';
        }

        private char _separator;
        private StreamReader _stream;
        private int _pos;
        private string[] _line;

        #region get a element

        public string Next()
        {
            if (_pos >= _line.Length)
            {
                _line = _stream.ReadLine().Split(_separator);
                _pos = 0;
            }

            return _line[_pos++];
        }

        public int NextInt()
        {
            return int.Parse(Next());
        }

        public long NextLong()
        {
            return long.Parse(Next());
        }

        public double NextDouble()
        {
            return double.Parse(Next());
        }

        #endregion

        #region convert array

        private int[] ToIntArray(string[] array)
        {
            var result = new int[array.Length];
            for (int i = 0; i < array.Length; i++)
            {
                result[i] = int.Parse(array[i]);
            }

            return result;
        }

        private long[] ToLongArray(string[] array)
        {
            var result = new long[array.Length];
            for (int i = 0; i < array.Length; i++)
            {
                result[i] = long.Parse(array[i]);
            }

            return result;
        }

        private double[] ToDoubleArray(string[] array)
        {
            var result = new double[array.Length];
            for (int i = 0; i < array.Length; i++)
            {
                result[i] = double.Parse(array[i]);
            }

            return result;
        }

        #endregion

        #region get row elements

        #region get array

        public string[] Array()
        {
            if (_pos >= _line.Length)
                _line = _stream.ReadLine().Split(_separator);

            _pos = _line.Length;
            return _line;
        }

        public int[] IntArray()
        {
            return ToIntArray(Array());
        }

        public long[] LongArray()
        {
            return ToLongArray(Array());
        }

        public double[] DoubleArray()
        {
            return ToDoubleArray(Array());
        }

        #endregion

        #region get 2~4 elements

        public void GetRow(out string a, out string b)
        {
            a = Next();
            b = Next();
        }

        public void GetRow(out string a, out string b, out string c)
        {
            a = Next();
            b = Next();
            c = Next();
        }

        public void GetRow(out string a, out string b, out string c, out string d)
        {
            a = Next();
            b = Next();
            c = Next();
            d = Next();
        }

        public void GetIntRow(out int a, out int b)
        {
            a = NextInt();
            b = NextInt();
        }

        public void GetIntRow(out int a, out int b, out int c)
        {
            a = NextInt();
            b = NextInt();
            c = NextInt();
        }

        public void GetIntRow(out int a, out int b, out int c, out int d)
        {
            a = NextInt();
            b = NextInt();
            c = NextInt();
            d = NextInt();
        }

        public void GetLongRow(out long a, out long b)
        {
            a = NextLong();
            b = NextLong();
        }

        public void GetLongRow(out long a, out long b, out long c)
        {
            a = NextLong();
            b = NextLong();
            c = NextLong();
        }

        public void GetLongRow(out long a, out long b, out long c, out long d)
        {
            a = NextLong();
            b = NextLong();
            c = NextLong();
            d = NextLong();
        }

        public void GetDoubleRow(out double a, out double b)
        {
            a = NextDouble();
            b = NextDouble();
        }

        public void GetDoubleRow(out double a, out double b, out double c)
        {
            a = NextDouble();
            b = NextDouble();
            c = NextDouble();
        }

        public void GetDoubleRow(out double a, out double b, out double c, out double d)
        {
            a = NextDouble();
            b = NextDouble();
            c = NextDouble();
            d = NextDouble();
        }

        #endregion

        #endregion

        #region get 2~4 column elements

        public void GetColumn(int n, out string[] a)
        {
            a = new string[n];
            for (int i = 0; i < n; i++)
            {
                a[i] = Next();
            }
        }

        public void GetColumn(int n, out string[] a, out string[] b)
        {
            a = new string[n];
            b = new string[n];
            for (int i = 0; i < n; i++)
            {
                GetRow(out a[i], out b[i]);
            }
        }

        public void GetColumn(int n, out string[] a, out string[] b, out string[] c)
        {
            a = new string[n];
            b = new string[n];
            c = new string[n];
            for (int i = 0; i < n; i++)
            {
                GetRow(out a[i], out b[i], out c[i]);
            }
        }

        public void GetColumn(int n, out string[] a, out string[] b, out string[] c, out string[] d)
        {
            a = new string[n];
            b = new string[n];
            c = new string[n];
            d = new string[n];
            for (int i = 0; i < n; i++)
            {
                GetRow(out a[i], out b[i], out c[i], out d[i]);
            }
        }

        public void GetIntColumn(int n, out int[] a)
        {
            string[] sa;
            GetColumn(n, out sa);
            a = ToIntArray(sa);
        }

        public void GetIntColumn(int n, out int[] a, out int[] b)
        {
            string[] sa, sb;
            GetColumn(n, out sa, out sb);
            a = ToIntArray(sa);
            b = ToIntArray(sb);
        }

        public void GetIntColumn(int n, out int[] a, out int[] b, out int[] c)
        {
            string[] sa, sb, sc;
            GetColumn(n, out sa, out sb, out sc);
            a = ToIntArray(sa);
            b = ToIntArray(sb);
            c = ToIntArray(sc);
        }

        public void GetIntColumn(int n, out int[] a, out int[] b, out int[] c, out int[] d)
        {
            string[] sa, sb, sc, sd;
            GetColumn(n, out sa, out sb, out sc, out sd);
            a = ToIntArray(sa);
            b = ToIntArray(sb);
            c = ToIntArray(sc);
            d = ToIntArray(sd);
        }

        public void GetLongColumn(int n, out long[] a)
        {
            string[] sa;
            GetColumn(n, out sa);
            a = ToLongArray(sa);
        }

        public void GetLongColumn(int n, out long[] a, out long[] b)
        {
            string[] sa, sb;
            GetColumn(n, out sa, out sb);
            a = ToLongArray(sa);
            b = ToLongArray(sb);
        }

        public void GetLongColumn(int n, out long[] a, out long[] b, out long[] c)
        {
            string[] sa, sb, sc;
            GetColumn(n, out sa, out sb, out sc);
            a = ToLongArray(sa);
            b = ToLongArray(sb);
            c = ToLongArray(sc);
        }

        public void GetLongColumn(int n, out long[] a, out long[] b, out long[] c, out long[] d)
        {
            string[] sa, sb, sc, sd;
            GetColumn(n, out sa, out sb, out sc, out sd);
            a = ToLongArray(sa);
            b = ToLongArray(sb);
            c = ToLongArray(sc);
            d = ToLongArray(sd);
        }

        public void GetDoubleColumn(int n, out double[] a)
        {
            string[] sa;
            GetColumn(n, out sa);
            a = ToDoubleArray(sa);
        }

        public void GetDoubleColumn(int n, out double[] a, out double[] b)
        {
            string[] sa, sb;
            GetColumn(n, out sa, out sb);
            a = ToDoubleArray(sa);
            b = ToDoubleArray(sb);
        }

        public void GetDoubleColumn(int n, out double[] a, out double[] b, out double[] c)
        {
            string[] sa, sb, sc;
            GetColumn(n, out sa, out sb, out sc);
            a = ToDoubleArray(sa);
            b = ToDoubleArray(sb);
            c = ToDoubleArray(sc);
        }

        public void GetDoubleColumn(int n, out double[] a, out double[] b, out double[] c, out double[] d)
        {
            string[] sa, sb, sc, sd;
            GetColumn(n, out sa, out sb, out sc, out sd);
            a = ToDoubleArray(sa);
            b = ToDoubleArray(sb);
            c = ToDoubleArray(sc);
            d = ToDoubleArray(sd);
        }

        #endregion

        #region get matrix

        public string[][] GetMatrix(int h)
        {
            string[][] result = new string[h][];
            for (int i = 0; i < h; i++)
            {
                result[i] = Array();
            }

            return result;

        }

        public int[][] GetIntMatrix(int h)
        {
            int[][] result = new int[h][];
            for (int i = 0; i < h; i++)
            {
                result[i] = IntArray();
            }

            return result;
        }

        public long[][] GetLongMatrix(int h)
        {
            long[][] result = new long[h][];
            for (int i = 0; i < h; i++)
            {
                result[i] = LongArray();
            }

            return result;
        }

        public double[][] GetDoubleMatrix(int h)
        {
            double[][] result = new double[h][];
            for (int i = 0; i < h; i++)
            {
                result[i] = DoubleArray();
            }

            return result;
        }

        public char[][] GetCharMatrix(int h)
        {
            char[][] result = new char[h][];
            for (int i = 0; i < h; i++)
            {
                result[i] = Next().ToCharArray();
            }

            return result;
        }

        #endregion
    }

    class UnionFind
    {
        private int[] Par, Rank;
        public UnionFind(int max)
        {
            Par = new int[max];
            Rank = new int[max];
            for (int i = 0; i < max; i++)
            {
                Par[i] = i;
            }
        }

        public int Find(int n)
        {
            if (Par[n] == n)
            {
                return n;
            }
            else
            {
                return Find(Par[n]);
            }
        }

        public bool Same(int a, int b)
        {
            return Find(a) == Find(b);
        }

        public void Union(int a, int b)
        {
            a = Find(a);
            b = Find(b);
            if (a == b) return;
            if (Rank[a] < Rank[b])
            {
                Par[a] = b;
            }
            else
            {
                Par[b] = a;
                if (Rank[a] == Rank[b]) Rank[a]++;
            }
        }
    }

    class Program
    {

        public void Solve()
        {
            var sc = new Scanner();
            long N, P;
            N = sc.NextLong();
            P = sc.NextLong();
            if (N == 1)
            {
                Console.WriteLine(P);
                return;
            }

            long ans = 1;
            for (int i = 2; i * i <= P; i++)
            {
                if (P % i == 0)
                {
                    int cnt = 0;
                    while (P % i == 0)
                    {
                        P /= i;
                        cnt++;
                    }

                    ans *= Pow(i, cnt / N);
                }
            }
            Console.WriteLine(ans);
        }

        private long Pow(long x, long y)
        {
            long ans = 1;
            for (int i = 0; i < y; i++)
            {
                ans *= x;

            }

            return ans;
        }


        static void Main(string[] args) => new Program().Solve();
    }
}