Problem:
Score : 400 points

Problem Statement

You are given positive integers N and M.

How many sequences a of length N consisting of positive integers satisfy a_1 \times a_2 \times ... \times a_N = M? Find the count modulo 10^9+7.

Here, two sequences a' and a'' are considered different when there exists some i such that a_i' \neq a_i''.

Constraints

All values in input are integers.

1 \leq N \leq 10^5

1 \leq M \leq 10^9

Input

Input is given from Standard Input in the following format:

N M

Output

Print the number of the sequences consisting of positive integers that satisfy the condition, modulo 10^9 + 7.

Sample Input 1

2 6

Sample Output 1

4

Four sequences satisfy the condition: \{a_1, a_2\} = \{1, 6\}, \{2, 3\}, \{3, 2\} and \{6, 1\}.

Sample Input 2

3 12

Sample Output 2

18

Sample Input 3

100000 1000000000

Sample Output 3

957870001

Solution in C# (Mono 4.6.2.0) (judge verdict: Runtime Error)

using System;
using System.Linq;
using System.Collections;
using System.Collections.Generic;

class Program
{
    static int Mod = 1000000007;

    static Dictionary<int,int> Factorize(int M)
    {
        Dictionary<int, int> r = new Dictionary<int, int>();
        while (M % 2 == 0)
        {
            M = (M - (M % 2)) / 2;
            if (r.ContainsKey(2))
                r[2]++;
            else
                r.Add(2, 1);
        }
        for(int i = 3; i <= M; i += 2)
        {
            while (M % i == 0)
            {
                M = (M - (M % i)) / i;
                if (r.ContainsKey(i))
                    r[i]++;
                else
                    r.Add(i, 1);
            }
        }
        return r;
    }
        
    public static void Main()
    {
        string[] s = Console.ReadLine().Split(' ');
        int N = int.Parse(s[0]);
        int M = int.Parse(s[1]);

        var r = Factorize(M);

        int maxduality = r.Max(x => x.Value);

        int[][] dp = new int[maxduality + 1][];
        for (int i = 0; i <= maxduality; i++)
            dp[i] = new int[N + 1];

        for (int i = 0; i <= N; i++)
        {
            dp[1][i] = i;
            dp[0][i] = i;
        }
        for (int i = 0; i <= maxduality; i++)
        {
            dp[i][1] = 1;
            dp[i][0] = 1;
        }
        for(int i = 2; i <= maxduality; i++)
        {
            for (int j = 2; j <= N; j++)
            {
                dp[i][j] = (dp[i - 1][j] + dp[i][j - 1]) % Mod;
            }
        }
        int q = 1;
        foreach (var i in r)
        {
            q = (q * dp[i.Value][N]) % Mod;
        }
        Console.WriteLine(q);
    }
}