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 PyPy3 (2.4.0) (judge verdict: Time Limit Exceeded)

def main():
    x,y = map(int,input().split())
    tmp = []
    for i in range(2,max(2,min(int(x // 2)+1, int(y //2 )+1))):
        if x % i ==0 and y % i == 0:
            tmp.append(i)
            while True:
                if x % i == 0:
                    x = x//i
                else:
                    break
            while True:
                if y % i == 0:
                    y = y//i
                else:
                    break


    print(len(tmp) + 1)
    # print(tmp)
    # for i,a in enumerate(tmp):
    #     if a < 4:
    #         tmp[i] = 1
    #         continue
    #     j = 2
    #     for j in range(2,int(a**0.5)+1):
    #         if a % j == 0:
    #             tmp[i] = 0
    #             break
    #     if tmp[i] != 0:
    #         tmp[i] = 1
    # print(sum(tmp))
    # print(tmp)

    # cnt = 0
    # # print(tmp)
    # flg = 0
    # for i,a in enumerate(tmp):
    #     # print('out' + str(i) + ' ' + str(a))
    #     if a == 1:
    #         continue
    #     leng = len(tmp)
    #     for j in range(i+1,leng):
    #         # print(j)
    #         # print(tmp)
    #         # print(leng)
    #         if flg == 1:
    #             j -=1
    #         flg = 0
    #         if j >= leng:
    #             break
    #         # print(str(j) + ' ' + str(leng) + ' ' + str(tmp[j]))
    #         if tmp[j] % a == 0:
    #             tmp.pop(j)
    #             leng -=1
    #             j -= 1
    #             # print(tmp)
    #             # print(j)
    #             flg = 1
    #
    #                 # print(j)
    #                 # print(a)
    #

    # print(len(tmp))
    # print(tmp)
if __name__=='__main__':
    main()