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.

Examples

Input

2 6

Output

4

Input

3 12

Output

18

Input

100000 1000000000

Output

957870001

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