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: Accepted)

def comb(n, k)
  res = 1
  i = n
  while i >= n-k+1
    res *= i
    i -= 1
  end
  while k > 0
    res /= k
    k -= 1
  end
  res
end
MOD = 10**9+7
n, m = gets.split.map(&:to_i)
i = 2
f = Hash.new(0)
while i * i <= m
  while m % i == 0
    m /= i
    f[i] += 1
  end
  i += 1
end
f[m] = 1 if m != 1
ans = 1
f.each do |k,v|
  ans *= comb(n+v-1, v)
  ans %= MOD
end
p ans