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 Julia (0.5.0) (judge verdict: Accepted)

N,M=map(x->parse(Int,x),split(readline()))
i=2
ans=1
mod=10^9+7
p(a,b)=b>0 ? p(a*a%mod,b>>1)*(b%2>0 ? a : 1)%mod : 1
function comb(a,b)
	x=y=1
	for i=1:b
		y=y*i%mod
		x=x*(a-i+1)%mod
	end
	x*p(y,mod-2)%mod
end
while i*i<=M
	c=0
	while M%i==0
		c+=1
		M=div(M,i)
	end
	ans=ans*comb(c+N-1,c)%mod
	i+=1
end
if M>1
	ans=ans*N%mod
end
println(ans)