Factorization

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

inputFormat

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

outputFormat

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

样例

3 12

18