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 Python (3.4.3) (judge verdict: Accepted)

A,B = map(int, input().split())




def getPrimeFactorsList(num):
  pn = 2 #素数は2から
  pflist = [] #素因数のリスト
  while pn * pn <= num: #√numまで調べる
    while num % pn == 0: #現在の素数で割り切れる範囲でループ
      num = num / pn
      pflist.append(pn)
    pn += 1 #割り切れなくなったら次の素数へ
  if num > 1:
    pflist.append(int(num))
    
  return pflist

pf_A = getPrimeFactorsList(A)
pf_B = getPrimeFactorsList(B)
ans = len(set(pf_A) & set(pf_B)) + 1
print(ans)