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' $\neq a_i$''.

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.

Constraints

• All values in input are integers.
• $1 \leq N \leq 10^5$
• $1 \leq M \leq 10^9$

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

见题面 Input 部分

见题面 Output 部分