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: Accepted)

# -*- coding: utf-8 -*-
A, B = map(int,input().split())
import fractions

def make_divisors(n):
  divisors = []
  for i in range(1, int(n**0.5)+1):
    if n % i == 0:
      divisors.append(i)
      if i != n // i:
        divisors.append(n//i)
  # divisors.sort()
  return divisors

n1 = make_divisors(A)
n2 = make_divisors(B)

answer = 0
n1_n2_set = set(n1) & set(n2)
n1_n2_list = list(n1_n2_set)
common_fractions = sorted(n1_n2_list)
# print(common_fractions)
varL = []
for i in range(len(common_fractions)):
  varsum = 0
  if len(varL) >= 1:
    for j in range(len(varL)):
      # print(common_fractions[i], varL[j], fractions.gcd(common_fractions[i], varL[j]))
      if fractions.gcd(common_fractions[i], varL[j]) != 1:
        varsum += 1
    if varsum == 0:
      answer += 1
      varL.append(common_fractions[i])
  else:
    varL.append(common_fractions[i])
    answer += 1

print(answer)