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 PyPy3 (2.4.0) (judge verdict: Accepted)

import math

def prime_division(n):
    ans = []
    m = int(n ** 0.5)
    i = 2
    while i <= m:
        if n % i == 0:
            cnt = 0
            while n % i == 0:
                n //= i
                cnt += 1
            ans.append((i, cnt))
            m = int(n ** 0.5)
        i += 1
    if n != 1:
        ans.append((n, 1))
    return ans

#  aabaaba  count+(N-1) C (N-1)

N,M=map(int,input().split())
pms=prime_division(M)
ans = 1
for pm in pms:
    #print(pm)
    ans *= math.factorial(pm[1]+(N-1)) // (math.factorial(pm[1]) * math.factorial(N-1))

print(ans % (10 ** 9 + 7))