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 PyPy3 (2.4.0) (judge verdict: Runtime Error)

import math

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

maxn=10**6
prime=[1]*(maxn+1)
prime[0]=0
prime[1]=0

for i in range(2,maxn+1):
    if prime[i]==0:
        continue

    for j in range(2,maxn//i+1):
        prime[i*j]=0

C=math.gcd(A,B)
cnt=1

for i in range(2,maxn+1):
    if prime[i]==0:
        continue

    if C%i==0:
        while C%i==0:
            C//=i
        cnt+=1

if C>1:
    cnt+=1

print(cnt)