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 {
public static void main(String[] args){
  Scanner sc = new Scanner(System.in);
  // 整数の入力
  long A = sc.nextLong();
  long B =sc.nextLong();
  List<Long> sosus = new ArrayList<Long>();
  long count = 1;
  if(A>B){
   for(long i=2;i<B;i++){
     if(sosuu(i,sosus)){
       sosus.add(i);
       if(A%i==0&&B%i==0){
         count++; 
       }
  	 }
   }
    if(sosuu(B,sosus)&&B>1){
       if(A%B==0){
         count++; 
       }
    }
  }else{
   for(long i=2;i<A;i++){
     if(sosuu(i,sosus)){
       sosus.add(i);
       if(A%i==0&&B%i==0){
         count++; 
       }
  	 }
   }
   if(sosuu(A,sosus)&&A>1){
       if(B%A==0){
         count++; 
       }
    }
  }

  System.out.print(count);
} 

   //素数判定的なあれ
	public static  boolean sosuu(Long lon,List<Long> sosus){
      long start=1L;
      if(lon<4){
       return true; 
      }
      for(long sosu:sosus){
          if(lon%sosu==0){
            return false;
          }
        if(sosu*sosu>lon){
          return true;
        }
        start = sosu;
      }
		for (long i = start+1; i*i < lon; ++i) {
			if(lon%i==0){
             return false;
            }
		}
      return true;
	}

  
}