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: Time Limit Exceeded)

#import sys

#input = sys.stdin.readline

#import heapq
import math
import fractions

def sosuhante(n):
    for k in range(2, int(math.sqrt(n))+1):
        if n% k ==0:
            return False
    return True

def main():
#    h,w,a,b = map(int, input().split())
    a,b=map(int,input().split())
    m=2
    k=1

    count=1
    if a>b:
        a,b=b,a
    sosu=set()
    #d = math.gcd(a,b)
#    print(d)
    c=math.sqrt(a)+1
 #   print(c)
    while m<=a:
        if a%m==0:
            sosu.add(m)
            if b%m==0:
                count+=1
            while a%m==0:
                a//=m

        m+=1
#    if sosuhante(a):
  #      if a not in sosu:
  #          if b%a==0:
  #              count+=1

#    print(sosu)
#    for i in sosu:
 #       if b%i==0:
 #           count+=1



    print(count)
#    for i in range(h):
#            print(aaa)

if __name__ == "__main__":
    main()