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)

# -*- coding: utf-8 -*-
"""
Created on Sun Sep 23 22:00:37 2018
ABC110D
@author: maezawa
"""
import collections

def comb(n, r):
    if n == 0 or r == 0:
        return 1
    return comb(n, r-1)*(n-r+1)//r

n, m = list(map(int, input().split()))

mod = 10**9+7
np = int(m**0.5 + 10)
is_prime = [True]*(np+1)

is_prime[0] = False
is_prime[1] = False

for i in range(2, np//2):
    if is_prime[i] == True:
        for j in range(2*i,np+1,i):
            is_prime[j] = False

prime_numbers = [i for i in range(np+1) if is_prime[i]]

pds = []
for i in prime_numbers:
    if m%i == 0:
        pds.append(i)
        md = m//i
        while md%i == 0:
            pds.append(i)
            md = md//i
        #pds.append(md)

#print(pds)
cpds = collections.Counter(pds)
#print(cpds)
ans = 1
for i in cpds.values():
    ans = ans*comb(n+i-1,i)%mod

print(ans)