10510: ABC110 —— D - Factorization
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Description
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 $a_i' \neq a_i''$.
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:
```
$N$ $M$
```
```
$N$ $M$
```
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.
- $1 \leq N \leq 10^5$
- $1 \leq M \leq 10^9$
- $1 \leq N \leq 10^5$
- $1 \leq M \leq 10^9$
Sample 1 Input
2 6
Sample 1 Output
4
Four sequences satisfy the condition: {$a_1,a_2$}={1,6},{2,3},{3,2} and {6,1}{6,1}.
Sample 2 Input
3 12
Sample 2 Output
18
Sample 3 Input
100000 1000000000
Sample 3 Output
957870001