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++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <iostream>
#include <map>

constexpr long long mod = 1000000007;

long long fact[1000001];

void fact_table()
{
	for (long long i = 1; i <= 1000000; i++)
		fact[i] = fact[i - 1] * i % mod;
}

long long pow(long long a, long long b)
{
	if (b == 0)
		return 1;
	if (b % 2 == 0)
	{
		long long half = pow(a, b / 2);
		return half * half % mod;
	}
	else
	{
		return a * pow(a, b - 1) % mod;
	}
}

long long inv(long long n)
{
	return pow(n, mod - 2);
}

long long comb(long long n, long long r)
{
	if (n - r < r)
		return comb(n, n - r);
	return fact[n] * inv(fact[n - r] * fact[r] % mod) % mod;
}

int main()
{
	long long N, M;
	std::cin >> N >> M;
	std::map<long long, long long> prime;
	for (long long i = 2; i * i <= M; i++)
	{
		while (M % i == 0)
		{
			if (prime.find(i) == prime.end())
				prime[i] = 1;
			else
				prime[i] = prime[i] + 1;
			M /= i;
		}
	}
	if (M != 1)
	{
		if (prime.find(M) == prime.end())
			prime[M] = 1;
		else
			prime[M] = prime[M] + 1;
	}
	fact[0] = 1;
	fact_table();
	long long ans = 1;
	for (auto p : prime)
	{
		ans *= comb(p.second + N - 1, N - 1);
		ans %= mod;
	}
	std::cout << ans << std::endl;
	return 0;
}