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: Runtime Error)

def xgcd(a, b):
    x0, y0, x1, y1 = 1, 0, 0, 1
    while b != 0:
        q, a, b = a // b, b, a % b
        x0, x1 = x1, x0 - q * x1
        y0, y1 = y1, y0 - q * y1
    return a
 
#targetまでの素数の数
import math
def sieve_of_eratosthenes2(target):
    dest = math.ceil(math.sqrt(target))
    target_list = [i for i in range(2, dest+2) if target%i==0]
    prime_num = 0
 
    while True:
        num_min = target_list[0]
        if num_min > dest:
            prime_num += len(target_list)
            break
        prime_num += 1        
        target_list = [i for i in target_list if i%num_min!=0]
        if target_list==[]:
            break
 
    return prime_num
 
a, b = map(int, input().split())
gcd = xgcd(a, b)
if gcd == 1:
    print(1)
else:
    ans = sieve_of_eratosthenes2(gcd)    
    print(ans+1)