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: Wrong Answer)

using System;
using System.Collections.Generic;
using System.IO;
using System.Linq;
using Int = System.Int64;

class C {
    static StreamWriter Out = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
    static void Main(string[] args) {
        Int N, P;
        Input(out N, out P);
        Int[] facts = Parse(P);
        Int ans = 1;
        for(Int i = 2; i < facts.Length; i++) {
            ans = Math.Max(ans * (facts[i] / N) * i, ans);
        }
        if(N == 1) {
            ans = P;
        }
        Print(ans);
        Out.Flush();
    }
    static Int[] Parse(Int N) {
        Int[] fact = new Int[1000000];
        Int max = 0;
        for(Int i = 2; i * i < N; i++) {
            while(N % i == 0) {
                fact[i]++;
                N = N / i;
                max = i;
            }
        }
        return fact.Take((int)max + 1).ToArray();
    }
    static T ChangeT<T>(string s) => (T)Convert.ChangeType(s, typeof(T));
    static void Input<A>(out A a) {
        var words = Console.ReadLine().Split(new[] { ' ' }, options: StringSplitOptions.RemoveEmptyEntries);
        a = ChangeT<A>(words[0]);
    }
    static void Input<A, B>(out A a, out B b) {
        var words = Console.ReadLine().Split(new[] { ' ' }, options: StringSplitOptions.RemoveEmptyEntries);
        a = ChangeT<A>(words[0]);
        b = ChangeT<B>(words[1]);
    }
    static void Input<A, B, C>(out A a, out B b, out C c) {
        var words = Console.ReadLine().Split(new[] { ' ' }, options: StringSplitOptions.RemoveEmptyEntries);
        a = ChangeT<A>(words[0]);
        b = ChangeT<B>(words[1]);
        c = ChangeT<C>(words[2]);
    }
    static void Input<A, B, C, D>(out A a, out B b, out C c, out D d) {
        var words = Console.ReadLine().Split(new[] { ' ' }, options: StringSplitOptions.RemoveEmptyEntries);
        a = ChangeT<A>(words[0]);
        b = ChangeT<B>(words[1]);
        c = ChangeT<C>(words[2]);
        d = ChangeT<D>(words[3]);
    }
    static void Input<A, B, C, D, E>(out A a, out B b, out C c, out D d, out E e) {
        var words = Console.ReadLine().Split(new[] { ' ' }, options: StringSplitOptions.RemoveEmptyEntries);
        a = ChangeT<A>(words[0]);
        b = ChangeT<B>(words[1]);
        c = ChangeT<C>(words[2]);
        d = ChangeT<D>(words[3]);
        e = ChangeT<E>(words[4]);
    }
    static void Input<A, B, C, D, E, F>(out A a, out B b, out C c, out D d, out E e, out F f) {
        var words = Console.ReadLine().Split(new[] { ' ' }, options: StringSplitOptions.RemoveEmptyEntries);
        a = ChangeT<A>(words[0]);
        b = ChangeT<B>(words[1]);
        c = ChangeT<C>(words[2]);
        d = ChangeT<D>(words[3]);
        e = ChangeT<E>(words[4]);
        f = ChangeT<F>(words[5]);
    }
    static void Input<T>(out T[] array) {
        array = Console.ReadLine().Split(new[] { ' ' }, options: StringSplitOptions.RemoveEmptyEntries).Select(s => ChangeT<T>(s)).ToArray();
    }
    static void Print<T>(T s) => Out.WriteLine(s);
    static void Print<T>(params T[] s) => Out.WriteLine(string.Join(" ", s));
    static void Print<T>(IEnumerable<T> e) => Out.WriteLine(string.Join(" ", e));
}