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 (GCC 5.4.1) (judge verdict: Accepted)

#include<stdio.h>
long long int prime(long long int n)
{
	if (n < 2)
		return n;
	long long int i;
	for (i = 2; i * i <= n; i++)
		if (n % i == 0)
			return i;
	return n;
}
long long int fact[200005];
long long int modpow(long long int a, long long int n, long long int p)
{
	if (n < 0)
		return 0;
	long long int res = 1;
	while (n > 0)
	{
		if (n % 2 > 0)
			res = res * a % p;
		a = a * a % p;
		n /= 2;
	}
	return res;
}
long long int comb(long long int n, long long int r, long long int p)
{
	if (n < 0 || r < 0 || n < r)
		return 0;
	long long int res = fact[n];
	res = res * modpow(fact[r], p - 2, p) % p;
	res = res * modpow(fact[n - r], p - 2, p) % p;
	return res;
}
int main()
{
	long long int n, m;
	scanf("%lld %lld", &n, &m);
	long long int ans = 1;
	long long int p = 1000000007;
	long long int c, q;
	fact[0] = 1;
	for (c = 1; c < 200005; c++)
		fact[c] = fact[c - 1] * c % p;
	while (m > 1)
	{
		q = prime(m);
		c = 0;
		while (m % q == 0)
		{
			c++;
			m /= q;
		}
		ans = ans * comb(c + n - 1, c, p) % p;
	}
	printf("%lld\n", ans);
	return 0;
}