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: Time Limit Exceeded)

A,B=input().split()
a=int(A)
b=int(B)
m=1
n=1
while n<=min(a,b):
  if a%n==0:
    if b%n==0:
      m=n
      n=n+1
    else:
      n=n+1
  else:
    n=n+1
if m==1:
  print(1)
elif m==2:
  print(2)
else:
  x=3
  u=0
  v=0
  while x<=m:
    t=2
    while t<=x-1:
      if x%t==0:
        u=u+1
        t=t+1
      else:
        u=u
        t=t+1
    if u==0:
      if m%x==0:
        v=v+1
      else:
        v=v
    else:
      v=v
    u=0
    x=x+1
  print(v+2)