Problem:
Score : 400 points

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

Solution in PHP7 (7.0.15) (judge verdict: Runtime Error)

<?php
define("MOD", 10**9+7);
fscanf(STDIN, "%d%d", $N, $M);

for($j = 2; $j <= $M; $j++){
    if($M%$j == 0){
        @$map[$j]++;
        $M/=$j;
        $j--;
    }
}
$product = 1;
foreach($map as $prime => $count){
    $product *= nCm($count + $N - 1, $count);
    $product %= MOD;
}
echo $product;