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 Python (3.4.3) (judge verdict: Wrong Answer)

def prime_factorization(number):
    l = []
    if number == 1:
        return l
    for i in range(2, int(number ** 0.5) + 2):
        count = 0
        while number % i == 0:
            count += 1
            number //= i
        if count != 0:
            l.append(count)
    if not l:
        l.append(1)        
    return l

def factorial(n):
    if n <= 1:
        return 1
    ans = 1
    for i in range(2, n+1):
        ans *= i
    return ans

def comb(n, m):
    ans = 1
    if m > n-m:
        m = n-m
    for i in range(m):
        ans *= n - i
    for i in range(1, m+1):
        ans //= i
    return ans

if __name__ == '__main__':
    mod = 10**9+7
    n, m = map(int, input().split())
    a = prime_factorization(m)
    answer = 1
    for x in a:
        answer *= comb(x+n-1, x)
        answer %= mod
    print(answer)