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.ArrayDeque;
import java.util.Scanner;

public class Main {
	
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		String[] inputArr = sc.nextLine().split(" ");
		long a = Long.parseLong(inputArr[0]);
		long b = Long.parseLong(inputArr[1]);
		sc.close();
		
		ArrayDeque<Long> divisorAList = new ArrayDeque<>();
		ArrayDeque<Long> divisorBList = new ArrayDeque<>();
		
		
		long dividedValue = a;
		for(long i = 2; i < a/2 && i <= dividedValue; i++) {
			if(dividedValue % i == 0) {
				divisorAList.add(new Long(i));
				while(dividedValue % i == 0) {
					dividedValue /= i;
				}
			}
		}
		
		dividedValue = b;
		for(long i = 2; i < b/2 && i <= dividedValue; i++) {
			if(dividedValue % i == 0) {
				divisorBList.add(new Long(i));
				while(dividedValue % i == 0) {
					dividedValue /= i;
				}
			}
		}
		
		int count = 1;// 1は絶対含む
		ArrayDeque<Long> smallQueue = null;
		ArrayDeque<Long> bigQueue = null;
		if(divisorAList.size() < divisorBList.size()) {
			smallQueue = divisorAList;
			bigQueue = divisorBList;
		}else {
			smallQueue = divisorBList;
			bigQueue = divisorAList;
		}
		
		while(!smallQueue.isEmpty() && !bigQueue.isEmpty()) {
			long smallQueueTop = smallQueue.pop();
			while(!bigQueue.isEmpty()) {
				if(smallQueueTop < bigQueue.peek()) {
					break;
				}
				long bigQueueTop = bigQueue.pop();
				if(smallQueueTop == bigQueueTop) {
					count++;
					break;
				}
			}
		}
		
		System.out.println(count);
	}

}