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 Ruby (2.3.3) (judge verdict: Runtime Error)

require 'prime'
MOD = 1_000_000_007
io = STDIN
n,m=io.gets.split.map(&:to_i)
def mul(range)
  range.to_a.inject(:*)
end
def comb(i,j)
  if i<2*j
    ret=comb(i,i-j)
  else
    ret=mul((i-j+1)..i)/mul(1..j)
  end
end

puts m.prime_division
 .map{|pr,ct|ct}
 .inject(1){|s,b|comb(b+n-1,b)*s%MOD}