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 Julia (0.5.0) (judge verdict: Accepted)

function main()
  n, m = map(s -> parse(BigInt, s), split(readline()))
  answer = BigInt(1)
  i = BigInt(2)
  while i * i <= m
    if mod(m, i) == 0
      count = BigInt(0)
      while mod(m, i) == 0
        count += 1
        m /= i
      end
      answer *= comb(n + count - 1, count)
    end
    i += 1
  end
  if m > 1
    answer *= n
  end
  println(mod(answer, BigInt(10^9 + 7)))
end

function comb(n::Integer, k::Integer)
  if n - k < k return comb(n, n - k) end
  numer = one(n)
  denom = one(n)
  for i = 0:k - 1
    numer = numer * (n - i)
    denom = denom * (i + 1)
  end
  return div(numer, denom)
end

main()