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 defaultdict, deque
from heapq import *
sys.setrecursionlimit(200000)
input = sys.stdin.readline

N, M, = map(int, input().split())
# N = int(input())
# L = [int(v) for v in input().split()]
# L = [[int(v) for v in input().split()] for _ in range(N)]
# L = [int(input()) for _ in range(N)]
# L = [list(input().strip())  for _ in range(N)]
# S = input().strip()

def gcd(a, b):
    if a < b:
        a, b = b, a
    if a % b == 0:
        return b
    return gcd(b, a % b)

g = gcd(N, M)

ans = set()
for i in range(2, int(g ** 0.5) + 1000000):
    while g % i == 0:
        ans.add(i)
        g = g // i

print(len(ans) + 1)