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.*;
import java.lang.*;

class Main {
	public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int A = sc.nextInt();
        int B = sc.nextInt();
        int n = 1;
        int a=  A;
        int b = B;

        for(int i = 2; Math.min(a,b) / 2 > i; i++){
            if(A % i ==0 && B % i == 0 && Main.primeNumber(i) == 0){
                n ++;
                A = A / i;
                B = B / i;
            System.out.println("i =" + i );
            System.out.println("A =" + A );
            System.out.println("B =" + B );

            }
        }

        System.out.println(n);

    }

    private static int primeNumber(int n) {
        for(int i = 2; i < n; i++) {
            if(n % i == 0) {
                return 1; //素数ではない
            }
        }
        return 0; //素数である
    }

}