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)


def sieve(n):
    nums = [i+1 for i in range(2, n, 2) if (i+1) % 3 != 0 and (i+1) % 5 !=0] # リスト内包表記で3,5の倍数をはじく
    ans = [2,3,5] # 3,5は素数なので加えてしまう
    while nums[0] <= n**0.5:
        for i in range(nums[0]**2, nums[-1]+1, nums[0]):
            if i in nums: nums.remove(i)
            ans.append(nums.pop(0))
            ans += nums
    return ans


A,B =map(int,input().split())
if A<B:
    A,B =B,A
foo = 1
while foo != 0:
    A,B = B, A%B
    #print(A,B)
    foo = B

#plis = sieve(1000)
#while p

plis = sieve(max(7,A))

foo =A

ans = 1
for p in plis:
    if  foo % p ==0:
        ans += 1
        foo = foo//p
        if foo < 1:
            break
print(ans)