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.*;
public class Main {
	Scanner sc = new Scanner(System.in);
	long a,b,c,d,e,f,k,l,m,n,x,y,z;
	long ans;
	long[] so;
	int sid = 1;

	Main(){
		// 整数の入力
		a = sc.nextLong();
		b = sc.nextLong();

		x = Math.max(a,b);
		y = Math.min(a,b);
		z = x%2==0?2:3;
		n = Math.min(y,x/z);

		so = new long[2000000];
		so[0]=1;

		for(long cnt=2;cnt<n;cnt++){
			if(a%cnt==0&&b%cnt==0){
				boolean flg = true;
				for(int ss=1;ss<sid;ss++){
					if(ko(cnt,so[ss])!=1){
						flg=false;
						break;
					}
				}
				if(flg){
					so[sid] = cnt;
					sid++;
				}
			}
		}

		// 出力
		System.out.print(sid);
	}

	public long ko(long x,long y){
		if(y==0)return x;
		return ko(y,x%y);
	}

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