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.*;

public class Main {
	Scanner sc = new Scanner(System.in);
	final int MOD = 1000000007;
	final int MAX = Integer.MAX_VALUE;
	final long LMAX = Long.MAX_VALUE;

	Set<Long> setA = new HashSet<>();
	Set<Long> setB = new HashSet<>();
	void doIt() {
		long a = sc.nextLong();
		long b = sc.nextLong();
		long len = a;
		setA.add(1l); setB.add(1l);
		for(long i = 2; i * i< len; i++) {
			while(a % i == 0) {
				a /= i;
				setA.add(i);
				//System.out.println(a + " " + i);
			}
		}
		setA.add(a);
		len = b;
		for(long i = 2; i * i < len; i++) {
			while(b % i == 0) {
				b /= i;
				setB.add(i);
			}
		}
		setB.add(b);
		long cnt = 0;
		for(long i : setA) {
			if(setB.contains(i)) {
				cnt++;
			}
		}
		//System.out.println(Arrays.toString(setA.toArray()));
		System.out.println(cnt);

	}



	public static void main(String[] args) {
		new Main().doIt();
	}
}