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: Wrong Answer)

package main
 
import (
	"bufio"
	"fmt"
	"log"
	"os"
	"strconv"
	"math"
)
 
func run() {
	n := nextFloat()
	k := nextInt()



	count := 0
	count2 := 0
	count3 := 0

	for i := 1; i <= int(math.Pow(n,0.5))+1; i++ {
		if(int(n) % i == 0 && k % i == 0 ){
			for j := 2; j <= int(math.Pow(float64(i),0.5))+1; j++ {
				if( i % j == 0){
					count2 ++
				}
			}
			if count2 > 0 {
				count3++
				count2 =0
			}
			count ++
		}
	}

	Println(count - count3)	
}

// --- template ---
// Thanks https://gist.github.com/halllllll/853ab587fd82ee3ffe6f7fb7fb499695
 
var sc = bufio.NewScanner(os.Stdin)
var out = bufio.NewWriter(os.Stdout)
 
// Caution: You will get unexpected result if a single token is larger than this size.
const BufferSize = 64 * 1024 * 1024
 

func gcd(a, b int) int {
    if b == 0 {
        return a
    } else {
        return gcd(b, a % b)
    }
}

func Print(a ...interface{}) (n int, err error) {
	return fmt.Fprint(out, a...)
}
 
func Printf(format string, a ...interface{}) (n int, err error) {
	return fmt.Fprintf(out, format, a...)
}
 

func readIntArray(n int) ([]int) {
	v := make([]int, 0)
	for i := 0; i < n; i++ {
		v = append(v, nextInt())
	}
	return v
}
 
func Println(a ...interface{}) (n int, err error) {
	return fmt.Fprintln(out, a...)
}
 
func next() string {
	sc.Scan()
	return sc.Text()
}
 
func nextInt() int {
	a, err := strconv.Atoi(next())
	if err != nil {
		log.Fatal(err)
	}
	return a
}
 
func nextFloat() float64 {
	a, err := strconv.ParseFloat(next(), 64)
	if err != nil {
		log.Fatal(err)
	}
	return a
}

 
func main() {
	sc.Buffer(make([]byte, 0, BufferSize), BufferSize)
	sc.Split(bufio.ScanWords)
	run()
	out.Flush()
}