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: Wrong Answer)

module Main where

import Data.Maybe (fromJust)
import Data.List
import Control.Monad
import qualified Data.ByteString.Char8 as BS

import qualified Data.Vector.Unboxed as VU
import qualified Data.Vector.Unboxed.Mutable as VUM

bytestr2Int = fst . fromJust . BS.readInt
getInt = bytestr2Int <$> BS.getLine
getIntL_H = map bytestr2Int. BS.words <$> BS.getLine
getIntL_V n = replicate n $ getInt
getInt2D n = replicate n $ getIntL_H

main :: IO ()
main = do
    [x,y] <- getIntL_H
    print . findPrimPair $ VU.fromList . factors $ gcd x y

findPrimPair vec = findPrimPairN vec $ VU.length vec - 1

findPrimPairN vec n 
    | 0 == length (findPrimPairCore vec n) = vec VU.! n
    | otherwise                            = findPrimPairN vec (n-1)

findPrimPairCore :: VU.Vector Int -> Int -> [()]
findPrimPairCore vec n = do
    tgt <- [0..(n-1)]
    guard ( 0 /= mod (vec VU.! n) (vec VU.! tgt) )
    pure ()

factors :: Int -> [Int]
factors n = [x | x <- [1..n], n `mod` x == 0]

prime :: Int -> Bool
prime n = factors n == [1, n]

primes :: Int -> [Int]
primes n = [x | x <- [2..n], prime x]