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 9.2.1) (judge verdict: Accepted)

#include <stdio.h>

#define Mod 1000000007

long long div_mod(long long x, long long y, long long z)
{
	if (x % y == 0) return x / y;
	else return (div_mod((1 + x / y) * y - x, (z % y), y) * z + x) / y;
}

long long combination(long long n, long long k)
{
	long long i, x, y;
	for (i = n, x = 1; i >= n - k + 1; i--) x = x * i % Mod;
	for (i = 2, y = 1; i <= k; i++) y = y * i % Mod;
	return div_mod(x, y, Mod);
}

int factorize(int n, int p[], int m[])
{
	int i, k;
	for (i = 2, k = 0; i * i <= n; i++) {
		if (n % i != 0) continue;
		p[k] = i;
		for (m[k] = 0; n % p[k] == 0; m[k]++, n /= p[k]);
		k++;
	}
	if (n > 1) {
		p[k] = n;
		m[k++] = 1;
	}
	return k;
}

int main()
{	
	int N, M;
	scanf("%d %d", &N, &M);
	if (N == 1 || M == 1) {
		printf("1\n");
		fflush(stdout);
		return 0;
	}

	int i, k, p[100], m[100];
	long long ans = 1;
	k = factorize(M, p, m);
	for (i = 0; i < k; i++) ans = ans * combination(N + m[i] - 1, m[i]) % Mod;
	printf("%lld\n", ans);
	fflush(stdout);
	return 0;
}