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: Accepted)

import java.io.*;
import java.math.*;
import java.util.*;
public class Main {

	public static void main(String[] args) {
		Scanner input = new Scanner(System.in);
		long A = input.nextLong();
		long B = input.nextLong();
		long limit = Math.min(A,B);
		long ans = 0;
		for (long i = 2; i <= Math.sqrt(limit); i++) {
			if (A%i==0&&B%i==0) ans++;
			while (A%i==0&&B%i==0) {
				A/=i;
				B/=i;
			}
		}
		if (GCD(A,B)>1) ans++; //Breaking case: 111 74
		ans++; //Including 1
		System.out.println(ans);
	}
	public static long GCD(long A, long B) {
		if (A==0||B==0) return Math.max(A, B);
		return GCD(Math.max(A, B)%Math.min(A, B),Math.min(A, B));
	}
}