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 PyPy2 (5.6.0) (judge verdict: Wrong Answer)

import math

N,M=map(int,raw_input().split())
m=int(math.sqrt(M))+2

mod=10**9+7
fact, inv_fact = [1], [1]
fact_tmp = 1
for i in range(1, 10**5+10000):
    fact_tmp *= i
    fact_tmp %= mod
    fact.append(fact_tmp)
    inv_fact.append(pow(fact_tmp, mod-2, mod))
 
 
def ncr(n,r):
	if n < 0 or r < 0 or n < r:
		return 0
	else:
		return (fact[n] * inv_fact[r] * inv_fact[n-r]) %mod

ans=1

for i in range(2,10**5):
	cnt=0
	while M%i==0:
		M/=i
		cnt+=1
	ans*=ncr(N+cnt-1,cnt)
	ans%=mod

print ans