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 collections as col
import numpy as np
import math as ma
import scipy.misc as spm #miscellaneous

MOD = 10**9 + 7
def inv(a): return pow(a, MOD-2, MOD)
def comb(n,r,MOD):
    ans = 1
    for i in range(r): # r-i==0でbreak
        ans *= n-i
        ans *= inv(r-i)
        ans %= MOD
    return ans


def prime(n):
    ans = []
    for i in range(2, int(n**0.5)+1):
        while not n%i: n //= i; ans.append(i)
    if n != 1: ans.append(n)
    return ans

n,m = map(int,input().split())
cnt = col.Counter(prime(m))

ans = 1
for key,val in cnt.items():
    #ans *= comb(val + n-1, n-1)
    ans *= comb(val + n-1, n-1, MOD)
    ans %= MOD
print(ans)