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 Perl (v5.18.2) (judge verdict: Time Limit Exceeded)

#!/usr/bin/env perl

use Math::BigInt;

$mod = 1_000_000_007;

chomp($_ = <STDIN>);
($n, $m) = split(/ /);

$res = 1;
for($p = 2;$p <= $m; $p++) {
  $b = 0;
  $v = Math::BigInt->new(1);
  while ($m % $p == 0) {
    $b++;
    $m /= $p;

    $v *= $n - 1 + $b;
    $v /= $b;
  }
  $res = $res * $v % $mod;
}

print $res;