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# (.NET Core 3.1.201) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.ComponentModel;
using System.Diagnostics.Contracts;
using System.IO;
using System.Linq;
using System.Numerics;
using System.Xml.Schema;
using System.Threading;
using System.Diagnostics.CodeAnalysis;
using System.Security.Cryptography;

namespace AtCoder
{
    public static class Ex
    {
        public static List<string> FastSort(this List<string> s) { s.Sort(StringComparer.OrdinalIgnoreCase); return s.ToList(); }
        public static void yesno(this bool b) { Console.WriteLine(b ? "yes" : "no"); }
        public static void YesNo(this bool b) { Console.WriteLine(b ? "Yes" : "No"); }
        public static void YESNO(this bool b) { Console.WriteLine(b ? "YES" : "NO"); }
        public static int BuildBitCount(this int bits)
        {
            bits = (bits & 0x55555555) + (bits >> 1 & 0x55555555);
            bits = (bits & 0x33333333) + (bits >> 2 & 0x33333333);
            bits = (bits & 0x0f0f0f0f) + (bits >> 4 & 0x0f0f0f0f);
            bits = (bits & 0x00ff00ff) + (bits >> 8 & 0x00ff00ff);
            return (bits & 0x0000ffff) + (bits >> 16 & 0x0000ffff);
        }
    }

    partial class AtCoder
    {
        public string GetStr() { return Console.ReadLine().Trim(); }
        public char GetChar() { return Console.ReadLine().Trim()[0]; }
        public int GetInt() { return int.Parse(Console.ReadLine().Trim()); }
        public long GetLong() { return long.Parse(Console.ReadLine().Trim()); }
        public double GetDouble() { return double.Parse(Console.ReadLine().Trim()); }
        public string[] GetStrArray() { return Console.ReadLine().Trim().Split(' '); }
        public int[] GetIntArray() { return Console.ReadLine().Trim().Split(' ').Select(int.Parse).ToArray(); }
        public long[] GetLongArray() { return Console.ReadLine().Trim().Split(' ').Select(long.Parse).ToArray(); }
        public char[] GetCharArray() { return Console.ReadLine().Trim().Split(' ').Select(char.Parse).ToArray(); }
        public double[] GetDoubleArray() { return Console.ReadLine().Trim().Split(' ').Select(double.Parse).ToArray(); }
        public T[][] CreateJaggedArray<T>(int H, int W, T value) { return Enumerable.Repeat(0, H).Select(s => Enumerable.Repeat(value, W).ToArray()).ToArray(); }
        public int[][] GetIntJaggedArray(int N) { return Enumerable.Repeat(0, N).Select(s => GetIntArray().ToArray()).ToArray(); }
        public long[][] GetLongJaggedArray(int N) { return Enumerable.Repeat(0, N).Select(s => GetLongArray().ToArray()).ToArray(); }
        public char[][] GetCharJaggedArray(int N) { return Enumerable.Repeat(0, N).Select(s => GetStr().ToCharArray()).ToArray(); }
        public double[][] GetDoubleJaggedArray(int N) { return Enumerable.Repeat(0, N).Select(s => GetDoubleArray()).ToArray(); }

        Dictionary<int, List<int>> GetUnweightedAdjacencyList(int N, int M, bool isDirected, bool isNode_0indexed)
        {
            var dic = new Dictionary<int, List<int>>();
            foreach (var e in Enumerable.Range(0, N)) { dic.Add(e, new List<int>()); }
            for (int i = 0; i < M; i++)
            {
                var input = GetIntArray();
                var a = isNode_0indexed ? input[0] : input[0] - 1;
                var b = isNode_0indexed ? input[1] : input[1] - 1;
                dic[a].Add(b);
                if (isDirected == false) dic[b].Add(a);
            }
            return dic;
        }
        Dictionary<int, List<Edge>> GetWeightedAdjacencyList(int N, int M, bool isDirected, bool isNode_0indexed)
        {
            var dic = new Dictionary<int, List<Edge>>();
            foreach (var e in Enumerable.Range(0, N)) { dic.Add(e, new List<Edge>()); }
            for (int i = 0; i < M; i++)
            {
                var input = GetIntArray();
                var a = isNode_0indexed ? input[0] : input[0] - 1;
                var b = isNode_0indexed ? input[1] : input[1] - 1;
                var c = input[2];
                dic[a].Add(new Edge(b, c));
                if (isDirected == false) dic[b].Add(new Edge(a, c));
            }
            return dic;
        }

        bool eq<T, U>() => typeof(T).Equals(typeof(U));
        T ct<T, U>(U a) => (T)Convert.ChangeType(a, typeof(T));
        T cv<T>(string s) => eq<T, int>() ? ct<T, int>(int.Parse(s))
                           : eq<T, long>() ? ct<T, long>(long.Parse(s))
                           : eq<T, double>() ? ct<T, double>(double.Parse(s))
                           : eq<T, char>() ? ct<T, char>(s[0])
                                             : ct<T, string>(s);
        void Multi<T>(out T a) => a = cv<T>(GetStr());
        void Multi<T, U>(out T a, out U b)
        {
            var ar = GetStrArray(); a = cv<T>(ar[0]); b = cv<U>(ar[1]);
        }
        void Multi<T, U, V>(out T a, out U b, out V c)
        {
            var ar = GetStrArray(); a = cv<T>(ar[0]); b = cv<U>(ar[1]); c = cv<V>(ar[2]);
        }
        void Multi<T, U, V, W>(out T a, out U b, out V c, out W d)
        {
            var ar = GetStrArray(); a = cv<T>(ar[0]); b = cv<U>(ar[1]); c = cv<V>(ar[2]); d = cv<W>(ar[3]);
        }
        void Multi<T, U, V, W, X>(out T a, out U b, out V c, out W d, out X e)
        {
            var ar = GetStrArray(); a = cv<T>(ar[0]); b = cv<U>(ar[1]); c = cv<V>(ar[2]); d = cv<W>(ar[3]); e = cv<X>(ar[4]);
        }
        void Multi<T, U, V, W, X, Y>(out T a, out U b, out V c, out W d, out X e, out Y f)
        {
            var ar = GetStrArray(); a = cv<T>(ar[0]); b = cv<U>(ar[1]); c = cv<V>(ar[2]); d = cv<W>(ar[3]); e = cv<X>(ar[4]); f = cv<Y>(ar[5]);
        }
    }

    class Edge
    {
        public Edge(int to, long length)
        {
            To = to;
            Length = length;
        }
        public int To { get; set; }
        public long Length { get; set; }
    }



    partial class Program
    {
        static void Main()
        {
            Console.SetOut(new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false });
            new AtCoder().Solve();
            Console.Out.Flush();
            Console.Read();
        }
    }

    public partial class AtCoder
    {
        public void Solve()
        {
            long N;long P;
            Multi(out N, out P);
            var factors = Factoring(P);
            long m = 1;
            foreach(var f in factors)
            {
                m *= (long)Math.Pow(f.Key, f.Value / N);
            }

            Console.WriteLine(m);
        }

        Dictionary<long, int> Factoring(long num)
        {
            Dictionary<long, int> vs = new Dictionary<long, int>();
            if (num == 1) { vs.Add(1, 1); return vs; }
            while (num % 2 == 0)
            {
                if (vs.ContainsKey(2) == false) { vs.Add(2, 0); }
                vs[2]++;
                num /= 2;

            }
            if (num == 1)
            {
                return vs;
            }
            long i = 3;
            while (i <= Math.Sqrt(num))
            {
                if (num % i == 0)
                {
                    if (vs.ContainsKey(i) == false) { vs.Add(i, 0); }
                    vs[i]++;
                    num /= i;
                }
                else
                {
                    i += 2;
                }
            }
            if (vs.ContainsKey(num) == false) { vs.Add(num, 1); }
            else { vs[num]++; }

            return vs;
        }
    }
}