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)

import sys
if sys.version_info.minor < 5:
    from fractions import gcd
else:
    from math import gcd
import math

DEBUG = True

A, B = map(int, input().split())
g = gcd(A, B)
if DEBUG:
    print("gcd(A, B): {}".format(g))

ans = [1]
i= 2
temp = g
while i <= int(-(-g**0.5//1))+1:
    if DEBUG:
        print("i: {}, g: {}".format(i, g))

    if g % i == 0:
        if DEBUG:
            print("This is a cd of A and B.")
        ans.append(i)

    while temp % i == 0:
        temp //= i

    i += 1

if DEBUG:
    print(ans)

print(len(ans))