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