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: Wrong Answer)


A,B =[int(x) for x in input().split()]

def bunkai(n):
    sosu= {1}
    tmp = n
    
    if tmp%2 == 0:
        while tmp%2==0:
            tmp //=2
        sosu.add(2)
    
    stop_flag = n//2

    for i in range(3,(n//2)+1,2):
        if tmp%i == 0:
            while tmp%i==0:
                tmp //=i
            sosu.add(i)
        if i > stop_flag:
            break
        else:
            stop_flag //=i 
            
    if tmp!=1:
        sosu.add(tmp)
                
    if sosu==[1]:
        sosu.add(n)
    
    return sosu

def check_sosu(n,x):
    ans=0
    tmp = n
    for i in x:
        if (tmp % i) == 0:
            ans+=1
    return ans

ans = check_sosu(B,bunkai(A))

print(ans)