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)

import math

def main():
    N,M = map(int,input().split())
    div_list = []
    d = 2
    ans = 1
    while M != 1:
        count = 0
        while M%d == 0:
            count += 1
            M //= d
        div_list.append(count)
        d += 1
    for i in div_list:
        a = math.factorial(i+N-1)
        b = math.factorial(i)
        c = math.factorial(N-1)
        ans *= (a//(b*c))%(10**9+7)
    print(ans%(10**9+7))

if __name__ == "__main__":
    main()