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 Perl (v5.18.2) (judge verdict: Time Limit Exceeded)

<>=~$";$\=1;$M=$';$m=1e9+7;
for(2..sqrt$'){
	$c=0;
	$M/=$_,$c++until$M%$_;
	$r=$d=1;
	$d=$d*$c--%$m,$r=$r*($`+$c)%$m while$c;
	$h=2e9+10;
	$r=$r*($h%2?$d:1)%$m,$d=$d*$d%$m while$h/=2;
	$\=$\*$r%$m;
}
$\=$\*$`%$m if$M>1;
print