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: Time Limit Exceeded)

from math import factorial

nm = input().split()
n = int(nm[0])
m = int(nm[1])

f = []

i = 2
j = 0
while (m > 1) and i<=m:
    while m%i == 0:
        m /= i
        j += 1
    if j >= 1:
        f.append(j)
    i += 1
    j = 0

        
ans = 1

for k in f:
    if k > 0:
        ans *= factorial(n+k-1) // (factorial(k) * factorial(n-1))
    
print(int(ans) % (10**9+7))