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(Int, s), split(readline()))
  mod = 10^9 + 7
  ans = 1
  i = 2

  while i * i <= m
    if m % i == 0
      count = 0
      while m % i == 0
        count += 1
        m /= i
      end
      ans *= comb(n + count - 1, count, mod)
      ans %= mod
    end
    i += 1
  end

  if m > 1
    ans *= n
    ans %= mod
  end

  println(ans)
end

function comb(n, k, m)
  if (n - k < k) return comb(n, n - k, m) end
  nume = 1
  deno = 1
  for i = 0:k - 1
    nume *= n - i
    deno *= i + 1
    nume %= m
    deno %= m
  end
  return (nume * modpow(deno, m - 2, m)) % m
end

function modpow(a, p, m)
  if p == 0
    return 1
  elseif p % 2 == 0
    return modpow(a, p / 2, m)^2 % m
  else
    return a * modpow(a, p - 1, m) % m
  end
end

main()