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 Go (1.6) (judge verdict: Time Limit Exceeded)

package main
 
import (
  "fmt"
)

//2つの入力値の最大公約数を返す
func max_div(num1 int, num2 int) int {
  
  if num1 < num2 {
    temp := num1
    num1 = num2
    num2 = temp
  }
  //ユークリッド互除法
  var rem int
  for { 
    rem = num1 % num2
    if rem == 0 {
      break
    }
    num1 = num2
    num2 = rem
  }
    return num2
}

func main() {
  
  var a,b int
  fmt.Scan(&a,&b)
  m := max_div(a,b)
  
  //A,Bの最大公約数の約数を求める
  var div []int
  count := 0

  //約数を保持
  for i := 1; i <= m; i++ {
    if m % i == 0 {
        div = append(div,i)
        count++
    }
  }

  ans := 1 //答えは必ず1以上
  var p bool
  p = true //素数
  
  //保持した約数と、その約数以下の値との最大公約数を計算
  for i := count-1; i > 0; i-- {
    for j := 2; j < i; j++ {
      //最大公約数が1以外ならその約数は素数ではない⇒探索終了
      if max_div(div[i],j) != 1 {
        p = !p
        break
      }
    }
    //最後までtrueなら素数
    if p {
      ans++
    }
    p = true
  }
  fmt.Println(ans)
}