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)

#coding: utf-8
import math
m,n = map(int,input().split())
ans = 1

# GCD(Grate Common Divisier) を求める
def gcd(x,y):
    if y==0:
        return x
    else:
        return gcd(y,x%y)

gcd_cnt = gcd(m,n)
# print(gcd_cnt)

# GCDの約数を素因数分解する
flg = 0
i = 2
aaa = gcd_cnt
while i <= gcd_cnt:
    # print(str(i)+str(',')+str(gcd_cnt))
    if gcd_cnt % i == 0:
        flg = 1
        gcd_cnt = gcd_cnt // i
    else:
        if flg == 1:
            ans +=1
            flg = 0
        i+=1
    if i > aaa/2:
        break
if flg == 1:
    ans += 1

# if m % 2 == 0 and n % 2 == 0:
#     div.append(2)

# for i in range(1,m+1):
#     # print(i)
#     if m % i == 0 and n % i == 0:
#         ans += 1
#         # m = m / i
#         # n = n / i
#         div.append(i)
#         # for j in range(2,len(div)):
#         #     if i % div[j] == 0:
#         #         flg = 1
#         #         break
#         # if flg == 0:
#         #     div.append(i)
#         # else:
#         #     flg = 0
    
# print(" ".join(map(str,div)))
# div.sorted(reversed=True)

# for j in range(1,div[0]):
#     div[0] % j


# # print(len(div))
print(ans)