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.io.PrintWriter;
import java.util.ArrayList;
import java.util.List;
import java.util.Scanner;

public class Main {

    static String br = System.getProperty("line.separator");
    static Scanner sc = new Scanner(System.in);
    static PrintWriter out = new PrintWriter(System.out);

    public static void main(String[] args) {
        int A = nextInt();
        int B = nextInt();

        int Answer = 1;

        int maxNum = 0;

        if (A != 0 && B != 0) {
	        if (A == B) {
	        	maxNum = A;
	        } else {
		        if (A >= B) {
		        	maxNum = gcd(A, B);
		        } else {
		        	maxNum = gcd(B, A);
		        }
	        }

	        List<Integer> list = new ArrayList<Integer>();

	        for (int i = 1; i<=maxNum; i++) {
	        	if (maxNum % i == 0) {
	        		list.add(i);
	        	}
	        }

	        for (int test : list) {
	        	if (isPrime(test)) {
	        		Answer += 1;
	        	}
	        }

	        println(Answer);
        } else {
        	println(0);
        }
    }

    static int nextInt() {
        return Integer.parseInt(next());
    }

    static Long nextLong() {
        return Long.parseLong(next());
    }

    static String next() {
        return sc.next();
    }

    static String nextLine(){
        return sc.nextLine();
    }

    static void println(Object o) {
        out.println(o);
        out.flush();
    }

    static void print(Object o) {
        PrintWriter out = new PrintWriter(System.out);
        out.print(o);
        out.flush();
    }

    public static boolean isPrime(int 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 = Math.sqrt(num);
        for (int 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;
    }

    static int gcd (int a, int b) {
    	int temp;
    	while((temp = a%b)!=0) {
    		a = b;
    		b = temp;
    	}
    	return b;
    }
}