Problem:
Score : 400 points

Problem Statement

Given are positive integers A and B.

Let us choose some number of positive common divisors of A and B.

Here, any two of the chosen divisors must be coprime.

At most, how many divisors can we choose?

Definition of common divisor

An integer d is said to be a common divisor of integers x and y when d divides both x and y.

Definition of being coprime

Integers x and y are said to be coprime when x and y have no positive common divisors other than 1.

Definition of dividing

An integer x is said to divide another integer y when there exists an integer \alpha such that y = \alpha x.

Constraints

All values in input are integers.

1 \leq A, B \leq 10^{12}

Input

Input is given from Standard Input in the following format:

A B

Output

Print the maximum number of divisors that can be chosen to satisfy the condition.

Sample Input 1

12 18

Sample Output 1

3

12 and 18 have the following positive common divisors: 1, 2, 3, and 6.

1 and 2 are coprime, 2 and 3 are coprime, and 3 and 1 are coprime, so we can choose 1, 2, and 3, which achieve the maximum result.

Sample Input 2

420 660

Sample Output 2

4

Sample Input 3

1 2019

Sample Output 3

1

1 and 2019 have no positive common divisors other than 1.

Solution in Haskell (GHC 7.10.3) (judge verdict: Time Limit Exceeded)

primes_til n = sieve (2: [3, 5 .. n])
primes = sieve (2: [3, 5..])
sieve [] = []
sieve (p:xs) = p : sieve [x | x <- xs, x `mod` p /= 0]

factors n l =
  [p | p <- l, p <= n, n `mod` p == 0]
  
merge [] _ = []
merge _ [] = []
merge (x:xs) (y:ys) =
  if x == y then
    x : merge xs ys
  else if x < y then
         merge xs (y:ys)
       else
         merge (x:xs) ys

main = do
  [a,b] <- map read . words <$> getLine
  let ps = primes_til (max a b)
  let facta = factors a ps
  let factb = factors b ps
  let ans_l  = 1 : merge facta factb 
  let ans = length ans_l
  putStrLn $ show ans