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: Time Limit Exceeded)

import java.util.*;
import static java.lang.Math.*;
import java.math.BigInteger;

public class Main {
	public static void main(String[] args){
		Scanner sc = new Scanner(System.in);
		
		// 入力
		long a = sc.nextLong();
		long b = sc.nextLong();
		long n = gcd(a,b);
		ArrayList<Long> list = new ArrayList<Long>();
		//System.out.println("n:" + n);
		// 計算
		long result = 1;
		for(long i = 1; i <= n; i++){
		    if(n%i > 0) continue;
		    int flg = 0;
		    for(Long j : list){
		        if(i%j == 0){
		            flg = 1;
		            break;
		        }
		    }
		    if(flg == 1) continue;
		    if(isPrime(i)){
		        //System.out.println("i:" + i);
		        list.add(i);
		        result++;
		    }
		}

		// 出力
		System.out.println(result);
        
	}
	
	static long gcd(long x, long y){
	    if(x < y){
	        long temp = x;
	        x = y;
	        y = temp;
	    }
	    if(y == 0) return x;
	    if(x%y == 0) return y;
	    return gcd(y , x%y);
	}
	
	public static boolean isPrime(long num) {
    if (num < 2) return false;
    else if (num == 2) return true;
    else if (num % 2 == 0) return false; // 偶数はあらかじめ除く

    double sqrtNum = sqrt(num);
    for (long i = 3; i <= sqrtNum; i += 2)
    {
        if (num % i == 0)
        {
            // 素数ではない
            return false;
        }
    }

    // 素数である
    return true;
    }
}