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 sys
readline = sys.stdin.readline
readlines = sys.stdin.readlines
sys.setrecursionlimit(10 ** 7)

import numpy as np
from fractions import gcd

# 1と素数をとる

A,B = map(int,readline().split())

D = gcd(A,B)

U = 10**6 + 100
is_prime = np.zeros(U,dtype=np.bool)
is_prime[2] = 1
is_prime[3::2] = 1
for p in range(int(U**.5)+10):
    if is_prime[p]:
        is_prime[p*p::p+p] = 0
primes = is_prime.nonzero()[0]

factor = primes[D%primes==0]

for p in factor:
    while D%p == 0:
        D //= p

answer = 1+len(factor)
if D != 1:
    answer += 1
print(answer)