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)

import math

a, b = map(int, input().split())

def gcd(x, y):
  z = x % y
  if z == 0:
    return y
  else:
    return gcd(y, z)
  
def common_divisors(x, y):
  xd = make_divisors(x)
  xd.append(1)
  xd.append(x)
  yd = make_divisors(y)
  yd.append(1)
  yd.append(y)
  return set(xd).intersection(yd)

def make_divisors(n):
  divisors = [] 
  for i in range(2, int(math.sqrt(n)) + 1):
    if n % i == 0:
      divisors.append(i)
      if i != n // i:
        divisors.append(n // i)
  return divisors

divisors = common_divisors(a, b)
divisors_set = frozenset(divisors)

res = []

for n in divisors:
  if n == 1 or n == 2 or n == 3:
    res.append(n)
  elif n % 2 == 0:
    continue
  else:
    dvs = set(make_divisors(n))
    if len(dvs) == 0 or not dvs <= divisors_set:
      res.append(n)

print("{}".format(len(res)))