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.Diagnostics;
using System.IO;
using System.Linq;
using System.Text;

namespace Caddi2018C
{
    class Program
    {
        public static void Solve(Input input)
        {
            var n = input.NextLong();
            var p = input.NextLong();
            var primes = Prime.PrimeFactors(p);
            var map = primes.GroupBy(x => x)
                .ToDictionary(x => x.Key, x => x.Count());

            long gcd = 1;
            foreach (var item in map)
            {
                if (item.Value < n) continue;

                gcd *= (long)Math.Pow(item.Key, (item.Value / n));
            }

            Console.WriteLine(gcd);
        }

        /// <summary>
        /// 素数判定
        /// 素因数分解
        /// 素数列挙（エラトステネスの篩）
        /// 約数列挙
        /// </summary>
        static class Prime
        {
            /// <summary>
            /// 素数か
            /// </summary>
            /// <param name="x"></param>
            /// <returns></returns>
            public static bool IsPrime(long x)
            {
                if (x < 2)
                {
                    return false;
                }
                if (x == 2)
                {
                    return true;
                }
                if ((x % 2) == 0)
                {
                    return false;
                }

                long rx = (long)(Math.Sqrt(x) + 1);
                for (long n = 3; n < rx; n += 2)
                {
                    if ((x % n) == 0)
                    {
                        return false;
                    }
                }

                return true;
            }

            /// <summary>
            /// 素数判定リスト
            /// </summary>
            /// <param name="n"></param>
            /// <returns></returns>
            public static bool[] PrimeSieve(int n)
            {
                // Sieve of Eratosthenes
                var sieve = Enumerable.Repeat<bool>(true, n + 1).ToArray();

                if (n > 2)
                {
                    sieve[0] = sieve[1] = false;
                }

                var rn = (int)(Math.Sqrt(n) + 1);
                foreach (var i in Enumerable.Range(2, rn - 2))
                {
                    if (sieve[i])
                    {
                        for (int j = 2 * i; j <= n; j += i)
                        {
                            sieve[j] = false;
                        }
                    }
                }

                return sieve;
            }

            /// <summary>
            /// 素数リスト
            /// </summary>
            /// <param name="n"></param>
            /// <returns></returns>
            public static IEnumerable<int> PrimeList(int n)
            {
                var sieve = PrimeSieve(n);

                return sieve.Select((x, i) => new { X = x, I = i })
                    .Where(x => x.X)
                    .Select(x => x.I);
            }

            /// <summary>
            /// 素因数分解
            /// </summary>
            /// <param name="n"></param>
            /// <returns></returns>
            public static IEnumerable<long> PrimeFactors(long n)
            {
                var m = n;
                var m2 = (long)Math.Sqrt(m) + 1;
                var p = 2;

                while (p < m2)
                {
                    if ((m % p) == 0)
                    {
                        m = m / p;
                        m2 = (long)Math.Sqrt(m) + 1;
                        yield return p;
                    }
                    else
                    {
                        p++;
                    }
                }
                if (m > 1)
                {
                    yield return m;
                }
            }

            /// <summary>
            /// n以下でnと互いに素な数の個数
            /// オイラーのファイ関数
            /// </summary>
            /// <param name="n"></param>
            /// <returns></returns>
            public static long PrimeCount(long n)
            {
                var primes = PrimeFactors(n).Distinct();

                var dsum = new decimal(1);
                foreach (var p in primes)
                {
                    var pp = new decimal(p);

                    dsum *= 1 - (1 / pp);
                }

                return (long)Math.Round(dsum * n);
            }

            /// <summary>
            /// 約数列挙 順番はバラバラなので注意！
            /// </summary>
            /// <param name="n"></param>
            /// <returns></returns>
            public static IEnumerable<long> Divisors(long n)
            {
                if (n < 1)
                {
                    yield break;
                }

                var rn = (int)(Math.Sqrt(n) + 1);
                for (long i = 1; i < rn; i++)
                {
                    if ((n % i) == 0)
                    {
                        yield return i;

                        if (i != (n / i))
                        {
                            yield return n / i;
                        }
                    }
                }
            }

            /// <summary>
            /// 約数列挙 昇順にソート
            /// </summary>
            /// <param name="n"></param>
            /// <param name="needsSort"></param>
            /// <returns></returns>
            public static IEnumerable<long> Divisors(long n, bool needsSort)
            {
                var divs = Divisors(n);

                if (needsSort)
                {
                    return divs.OrderBy(x => x);
                }
                else
                {
                    return divs;
                }
            }
        }

        #region Main
        public static void Main(string[] args)
        {
            // 出力が少ないときはこれをセットする方が時間かかるけれど
            // その場合は出力がボトルネックになっていないので、まあ良しとする
            var needsFlushOutput = true;
            if (needsFlushOutput)
            {
                // 細かく出力しないようにする
                var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
                Console.SetOut(sw);
            }

            // 通常は引数無しで、ファイルから読み出したい場合はpath指定する
            var input = new Input();
            // 仮想的に標準入力をセットする
            //input.SetText("");

            Solve(input);

            Console.Out.Flush();
        }
        #endregion

        #region Competitive Template
#pragma warning disable CS0414
        static readonly int MOD = (int)1e9 + 7;
        static readonly int[] dx = { 1, 0, -1, 0 };
        static readonly int[] dy = { 0, 1, 0, -1 };
        /// <summary> 左上が原点 </summary>
        static readonly char[] dir = { 'R', 'U', 'L', 'D' };
#pragma warning restore CS0414

        /// <summary>
        /// 値を書き換え可能なTuple（ぐらいのイメージ）
        /// </summary>
        public class Pair<T, U> : IComparable<Pair<T, U>>, IEquatable<Pair<T, U>>
            where T : IComparable<T>
            where U : IComparable<U>
        {
            public T V1 { get; set; }
            public U V2 { get; set; }

            public Pair(T v1, U v2)
            {
                this.V1 = v1;
                this.V2 = v2;
            }

            public Pair(Pair<T, U> src) : this(src.V1, src.V2) { }

            public int CompareTo(Pair<T, U> other)
            {
                var r = this.V1.CompareTo(other.V1);
                if (r == 0) r = this.V2.CompareTo(other.V2);

                return r;
            }

            public bool Equals(Pair<T, U> other)
                => (other != null && this.CompareTo(other) == 0);

            public override string ToString()
                => $"{V1} {V2}";

            public override bool Equals(object obj)
                => Equals(obj as Pair<T, U>);

            public override int GetHashCode()
            {
                var hashCode = 1989511945;
                hashCode = hashCode * -1521134295 + V1.GetHashCode();
                hashCode = hashCode * -1521134295 + V2.GetHashCode();
                return hashCode;
            }

            public static bool operator ==(Pair<T, U> a, Pair<T, U> b)
            {
                if (object.ReferenceEquals(a, null))
                {
                    return object.ReferenceEquals(b, null);
                }

                return a.Equals(b);
            }

            public static bool operator !=(Pair<T, U> a, Pair<T, U> b)
                => !(a == b);
            public static bool operator <(Pair<T, U> a, Pair<T, U> b)
                => a.CompareTo(b) < 0;
            public static bool operator <=(Pair<T, U> a, Pair<T, U> b)
                => a.CompareTo(b) <= 0;
            public static bool operator >(Pair<T, U> a, Pair<T, U> b)
                => a.CompareTo(b) > 0;
            public static bool operator >=(Pair<T, U> a, Pair<T, U> b)
                => a.CompareTo(b) >= 0;
        }

        public class Input
        {
            // 変な改行コードがたまに混じっているので、一応セパレート指定する
            // スペース単独指定の方がもちろん早い
            static readonly char[] separator = { ' ', '\r', '\n' };
            readonly StreamReader sr;
            Queue<string> q { get; set; }

            /// <summary>
            /// 特定のファイルから読み出したい場合はpath指定する
            /// </summary>
            public Input(string path = "")
            {
                q = new Queue<string>();

                if (string.IsNullOrEmpty(path))
                {
                    sr = new StreamReader(Console.OpenStandardInput());
                }
                else
                {
                    sr = new StreamReader(path);
                }
            }

            /// <summary>
            /// 入力予約
            /// </summary>
            public void SetText(IEnumerable<string> items)
            {
                foreach (var item in items)
                {
                    SetText(item);
                }
            }

            /// <summary>
            /// 入力予約
            /// </summary>
            public bool SetText(string s)
            {
                if (s == null) return false;

                foreach (var elem in s.Trim().Split(separator, StringSplitOptions.RemoveEmptyEntries))
                {
                    q.Enqueue(elem);
                }

                return true;
            }

            /// <summary>
            /// 要素が存在するか
            /// </summary>
            public bool Any()
                => q.Any() || read();


            /// <summary>
            /// 内部queueに入力からの値をsplitして格納する
            /// </summary>
            bool read()
            {
                if (!SetText(sr.ReadLine())) return false;

                if (!q.Any()) return read();

                return true;
            }

            /// <summary>
            /// 次のstringを一つ読み込む
            /// </summary>
            public string Next()
            {
                if (!q.Any() && !read())
                {
                    return "";
                }

                return q.Dequeue();
            }

            /// <summary>
            /// 指定個数queueにたまるまでenqueueし続ける
            /// </summary>
            bool accumulate(int n)
            {
                while (q.Count() < n)
                {
                    if (!read()) return false;
                }

                return true;
            }

            public int NextInt() => int.Parse(Next());
            public long NextLong() => long.Parse(Next());
            public double NextDouble() => double.Parse(Next());

            /// <summary>
            /// n個の要素をparseして、それぞれにoffsetをaddした配列を返す
            /// </summary>
            T[] NextT<T>(int n, T offset, Func<string, T> parse, Func<T, T, T> add)
            {
                if (!accumulate(n)) return null;

                var a = new T[n];

                for (int i = 0; i < n; i++)
                    a[i] = add(parse(q.Dequeue()), offset);

                return a;
            }

            public string[] Next(int n) => NextT(n, "", x => x, (x, y) => x);
            public int[] NextInt(int n, int offset = 0) => NextT(n, offset, int.Parse, (x, y) => x + y);
            public long[] NextLong(int n, long offset = 0) => NextT(n, offset, long.Parse, (x, y) => x + y);
            public double[] NextDouble(int n, double offset = 0.0) => NextT(n, offset, double.Parse, (x, y) => x + y);

            /// <summary>
            /// n2個の要素をn1個まとめたリストとする
            /// </summary>
            List<T>[] NextList<T>(int n1, int n2, T offset, Func<string, T> parse, Func<T, T, T> add)
            {
                if (!accumulate(n2 * n1)) return null;

                var list = Enumerable.Range(0, n1)
                    .Select(_ => new List<T>())
                    .ToArray();

                for (int i = 0; i < n1; i++)
                {
                    list[i].Add(add(parse(q.Dequeue()), offset));
                }

                return list;
            }

            public List<string>[] Next(int n1, int n2) => NextList(n1, n2, "", x => x, (x, y) => x);
            public List<int>[] NextInt(int n1, int n2, int offset = 0) => NextList(n1, n2, offset, int.Parse, (x, y) => x + y);
            public List<long>[] NextLong(int n1, int n2, long offset = 0) => NextList(n1, n2, offset, long.Parse, (x, y) => x + y);
            public List<double>[] NextDouble(int n1, int n2, double offset = 0.0) => NextList(n1, n2, offset, double.Parse, (x, y) => x + y);
        }

        static class Utils
        {
            public static void Print<T>(IEnumerable<T> ie, string sep = " ") => Console.WriteLine(string.Join(sep, ie));
            public static void Print<T>(params T[] objs) => Print(objs);
            public static T Max<T>(params T[] objs) => objs.Max();
            public static T Min<T>(params T[] objs) => objs.Min();

            public static void Swap<T>(ref T x, ref T y) where T : struct { var t = x; x = y; y = t; }
            public static void Swap<T>(IList<T> list, int i, int j) where T : struct { var t = list[i]; list[i] = list[j]; list[j] = t; }

            /// <summary>
            /// vでfillされたT[d1][d2]配列を作成する
            /// </summary>
            public static T[][] Create2DArray<T>(int d1, int d2, T v = default(T))
            {
                return
                    Enumerable.Repeat(0, d1).Select(_ =>
                    Enumerable.Repeat(v, d2).ToArray()).ToArray();
            }

            /// <summary>
            /// vでfillされたT[d1][d2][d3]配列を作成する
            /// </summary>
            public static T[][][] Create3DArray<T>(int d1, int d2, int d3, T v = default(T))
            {
                return
                    Enumerable.Repeat(0, d1).Select(_ =>
                    Enumerable.Repeat(0, d2).Select(__ =>
                    Enumerable.Repeat(v, d3).ToArray()).ToArray()).ToArray();
            }
        }
        #endregion
    }
}