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: Runtime Error)

import java.util.ArrayList;
import java.util.Scanner;

public class Main {
	public static void main(String[] args){

		Scanner sc = new Scanner(System.in);
		int a = sc.nextInt();
		int b = sc.nextInt();
		ArrayList<Integer> aList = new ArrayList<>();
		ArrayList<Integer> bList = new ArrayList<>();
		ArrayList<Integer> finalList = new ArrayList<>();
		int result = 0;

		//　aの約数を取得
		for(int i = 1; i <= a; i++) {
			if(a%i == 0) {
				aList.add(i);
			}
		}
		//　bの約数を取得、かつaとの公約数を取得
		for(int i = 1; i <= b; i++) {
			if((aList.contains(i)) && (b%i == 0)) {
				bList.add(i);
			}
		}
		//　公約数の中ですべての組み合わせを列挙
		for(int i = bList.size(); 0 <= i; i--) {
			ArrayList<Integer> resultList = new ArrayList<>();
			for(int h = i-1; 1 <= h; h--) {
				if(bList.get(i-1) % bList.get(h-1) == 0) {
					resultList.add(i);
				}
			}
			//　互いに素（割り切れるのは1のみ）になる場合のみ結果に入れる
			if(resultList.size() == 1) {
				finalList.add(i);
			}
		}
		
		//　1の場合を追加して出力
		System.out.print(finalList.size() + 1);
		sc.close();
	}
}