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 Java8 (OpenJDK 1.8.0) (judge verdict: Runtime Error)

import java.util.*;

class Main {
    public static void main(String args[]){
    	Scanner sc = new Scanner(System.in);
		// 整数の入力
		int A = sc.nextInt();
		int B = sc.nextInt();
		
		int tmp;
		while ((tmp = A % B) != 0) {
            A = B;
            B = tmp;
        }
		int res = 1;
		if(B > 1) {
			int i = 2;
			while(i <= B) {
				if(B % i == 0) {
					res++;
					B /= i;
					while(B % i == 0) {
						B /= i;
					}
				}
				i++;
			}
			
		}else {
			res = 1;
		}
		// 出力
		System.out.println(res);
    }
}