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: Accepted)

import java.util.*

tailrec fun gcd(x: Long, y: Long): Long = if (y == 0L) x else gcd(y, x % y)

fun factorize(n: Long): List<Pair<Long, Long>> {
    val list = ArrayList<Pair<Long, Long>>()
    var m = n
    var k = 2L

    while (m > 1 && k * k <= m) {
        var s = 0L
        while (m % k == 0L) {
            m /= k
            s++
        }
        if (s > 0) {
            list.add(Pair(k, s))
        }
        k++
    }

    if (m > 1) {
        list.add(Pair(m, 1L))
    }

    return list
}

fun main(args: Array<String>) {
    val (A, B) = readLine()!!.split(" ").map{it.toLong()}
    val g = gcd(A, B)

    println(factorize(g).size + 1)
}