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 JavaScript (Node.js 12.16.1) (judge verdict: Wrong Answer)

function factorization(a){
    var workbench=a;
    var i=2;
    var ret=[];
    while(a>1){
        if(workbench%i===0){
            ret.push(i);
            workbench/=i;
            continue;
        }
        if(i**2>workbench){
            ret.push(workbench);
            break;
        }
        i++;
    }
    return ret;
}

function Main(input) {
  input=input.split("\n");
  if(input[input.length-1]===''){
    input.pop();
  }
  const A=input[0].split(' ')[0]-0;
  const B=input[0].split(' ')[1]-0;
  var min=Math.min(A,B);
  var max=Math.max(A,B);
  var temp;
  while(min>0){
    temp=min;
    min=max%min;
    max=temp;
  }
  var ret=0;
  var previous=0;
  factorization(max).forEach(e=>{
    if(e!==previous){
      previous=e;
      ret++;
    }
  });
  console.log(ret+1);
}




//*この行以降は編集しないでください（標準入出力から一度に読み込み、Mainを呼び出します）
Main(require("fs").readFileSync("/dev/stdin", "utf8"));