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
from collections import deque
import math

A, B = map(int, sys.stdin.readline().split())
C, D = max(A, B), min(A, B)

#ユーグリッド互除法
while True:
    amari = C%D
    C, D = D, amari
    if amari ==0:
        gcd = C
        break
#print(gcd)

#素因数分解
L = deque([1])
n = int(math.sqrt(gcd))+1
#print(n)
for i in range(2, n+1):
    while True:
        if gcd%i ==0:
            L.append(i)
            gcd = gcd//i
        else:
            break
#print(L)
L = set(L)
print(len(L))