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: Wrong Answer)

import java.util.Scanner;

public class Main {
 
	public Main() {
		// TODO 自動生成されたコンストラクター・スタブ
	}
 
	public static void main(String[] args){
		Scanner sc = new Scanner(System.in);
		int n,k,count,m,index;
		long a,b,a2,b2,common,answer,c,i,j;
		String s,t;
		
			// 整数の入力
		
		a = sc.nextLong();
		b = sc.nextLong();
		sc.close();
		count=0;
		if(a==b) {
			common=a;
		}
		else {
			if(a<b) {
				c=a;
				a=b;
				b=c;
			}
			LoopA: for(;;) {
				c=a%b;
				if(c==0) {
					common=b;
					break LoopA;
				}
				a=b;
				b=c;
			}
		}
		//System.out.print(common);
		answer=0L;
		if(common==1) answer=1L; 
		else {
			answer=1L;
			LoopC: for(i=2;i<=common;) {
				if(common%i==0) {
					answer++;
					LoopB: for(;;) {
						common=common/i;
						if(common%i>0) break LoopB;
					}
				}
				if(i*i>common) {
					answer++;
					break LoopC;
				}
				if(i==2)i=3;
				else if(i==3)i=5;
				else if(i==5)i=7;
				else if(i==7)i=11;
				else if(i==11)i=13;
				else i=i+2;
			}
		}
		System.out.print(answer);

			// 出力
 
	}
}