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.util.*;
import java.lang.Math;

public class Main{
	
	static Scanner sc = new Scanner(System.in);
	
	public static void main(String[] args){
		long a = sc.nextLong();
		long b = sc.nextLong();
		
		if(a > b){
			long tmp = a;
			a = b;
			b = tmp;
		}
			
		double ub = Math.sqrt(a);
		List<Long> divisors = new ArrayList<>();
		for(long i = 1L; i <= ub; ++i){
			if(a % i == 0L){
				divisors.add(i);
				long qa = a / i;
				if(i != qa){
					divisors.add(qa);
				}
			}
		}
		
		int ans = divisors.size();
		for(int i = 0; i < divisors.size(); ++i){
			if(b % divisors.get(i) != 0L){
				divisors.set(i, 0L);
				--ans;
			}
		}
		
		Collections.sort(divisors);
		//System.out.println(divisors);
		
		for(int i = 0; i < divisors.size(); ++i){
			if(divisors.get(i) == 0L) continue;
			
			if(divisors.get(i) == 1L || i == divisors.size() - 1L) continue;
			
			for(int j = i + 1; j < divisors.size(); ++j){
				if(divisors.get(j) > 0L && divisors.get(j) % divisors.get(i) == 0L){
					divisors.set(j, 0L);
					--ans;
				}
			}
		}
		
		System.out.println(ans);
	}
}