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 Kotlin (1.0.0) (judge verdict: Time Limit Exceeded)

fun main(args: Array<String>) {
    val (a,b) = readLine()!!.split(" ").map(String::toLong)
    val x = gcd(a,b)
    val cnt = decom(x)
    println(cnt)
}

fun decom(x: Long) : Int {
    var value = x
    var cnt = 1
    var i = 2L
    while (i <= value) {
        if ( value % i == 0L) {
            cnt += 1
            while (value % i == 0L) {
                value /= i
            }
        } else {
            i += 1L
        }
    }
    return cnt
}

fun gcd(a : Long, b : Long) : Long {
    return if (a % b == 0L) b else gcd(b, a % b)
}