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.io.*;

public class Main
{
	public static void main(String [] Args)
	{
		Scanner in=new Scanner(System.in);
		int [] prime=new int [10000000];
		for(int i=2;i<10000000;i++)
		{
			if(prime[i]==0)
			{
				for(int j=2;i*j<10000000;j++)
				{
					prime[i*j]=1;
				}
			}
		}
				
		long a=in.nextLong();
		long b=in.nextLong();
		long q=gcd(a,b);
		int ans=1;
		long temp=q;
		if(q>10000000)
			q=10000000;
		for(int i=2;i*i<=q;i++)
		{
			if(temp%i==0&&prime[i]==0)
			{
				ans++;
				while(temp%i==0)
				{
					temp=temp/i;
				}
			}
			if(temp==1)
				break;
		}
		if(temp!=1)
		{
			ans++;
		}
		System.out.println(ans);
	}
	public static long gcd (long a,long b)
	{
		if(a%b==0)
			return b;
		return gcd(b,a%b);
	}
}