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: Wrong Answer)

import java.util.*;
import java.lang.*;
public class Main{

	public static long gcd(long x,long y){
		return y>0 ? gcd(y,x%y) : x;
	}

	public static void main(String[] args){
		Scanner sc = new Scanner(System.in);

		long A = sc.nextLong();
		long B = sc.nextLong();
		long max = gcd(A,B);
		long L = max;
		int count = 0;
		for( long i=2; i*i<=max; i++ ){
			if( L%i==0 ){
				count++;
			}
			while(L%i==0){
				L = L/i;
			}
		}
		if( max==2 ){
			count = 1;
		}
		if( max==3 ){
			count = 2;
		}
		System.out.println(count+1);
	}
}