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)

const MOD = Int64(10^9 + 7)

function main()
  n, m = map(s -> parse(Int64, s), split(readline()))
  answer = Int64(1)
  i = Int64(2)

  while i * i <= m
    if mod(m, i) == 0
      count = Int64(0)
      while mod(m, i) == 0
        count += 1
        m /= i
      end
      answer = mod(answer * modcomb(n + count - 1, count), MOD)
    end
    i += 1
  end

  if m > 1
    answer = mod(answer * n, MOD)
  end

  println(answer)
end

function modcomb(n::Integer, k::Integer)
  if n - k < k return modcomb(n, n - k) end
  numer = one(n)
  denom = one(n)
  for i = 0:k - 1
    numer = mod(numer * (n - i), MOD)
    denom = mod(denom * (i + 1), MOD)
  end
  return mod(numer * modpow(denom, MOD - 2), MOD)
end

function modpow(a::Integer, p::Integer)
  if p == 0
    return one(a)
  elseif mod(p, 2) == 0
    return mod(modpow(a, div(p, 2))^2, MOD)
  else
    return mod(a * modpow(a, p - 1), MOD)
  end
end

main()