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: Time Limit Exceeded)

import sys
from io import StringIO
import unittest
import math

class TestClass(unittest.TestCase):
    def assertIO(self, input, output):
        stdout, stdin = sys.stdout, sys.stdin
        sys.stdout, sys.stdin = StringIO(), StringIO(input)
        resolve()
        sys.stdout.seek(0)
        out = sys.stdout.read()[:-1]
        sys.stdout, sys.stdin = stdout, stdin
        self.assertEqual(out, output)
    def test_入力例_1(self):
        input = """12 18"""
        output = """3"""
        self.assertIO(input, output)
    def test_入力例_2(self):
        input = """420 660"""
        output = """4"""
        self.assertIO(input, output)
    def test_入力例_3(self):
        input = """1 2019"""
        output = """1"""
        self.assertIO(input, output)
def sosuu(N):
    mx = int(math.sqrt(N))
    target = [i for i in range(2,N+1)]
    pN= []
    while len(target)>0 and target[0] <= mx:
        pN.append(target[0])
        tmp = target[0]
        target = [i for i in target if i % tmp != 0]
    pN.extend(target)
    return pN


def resolve():
    (A,B)=(int(i) for i in input().split())
    N=min(A,B)
    count=0
    for i in sosuu(N):
        if A%i ==0 and B%i==0:
            count+=1        
    print(count+1)
    


if __name__ == "__main__":
    resolve()