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 Java7 (OpenJDK 1.7.0) (judge verdict: Time Limit Exceeded)

import java.util.*;

public class Main {

	static Map<Long, Boolean> map = new HashMap<Long, Boolean>();

	public static void iniprime(long len){
		map.put((long)0, false);
		map.put((long)1, false);
		map.put((long)2, true);
		for(long i = 2; i < len; ++i){
			if(map.get(i) == null || map.get(i) != false){
				map.put(i, true);
				for(long j = 2; i <= len / j; ++j){
					if(i >= Long.MAX_VALUE / j)break;
					map.put(i * j, false);
				}
			}
		}
	}

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		long a = sc.nextLong(), b = sc.nextLong();
		sc.close();
		long ans = 1;
		long n = Math.min(a, b);
		iniprime(n);
		for(long i = 2; i <= n; ++i){
			if(a % i == 0 && b % i == 0){
				boolean p = map.get(i);
				if(p)
				++ans;
			}
		}
		System.out.println(ans);
	}
}