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: Wrong Answer)

import java.lang.Math

fun main(args: Array<String>) {
    val (a, b) = readLine()!!.split(" ").map(String::toLong).sorted()

    val c = gcd(b, a)
    val factors = (2L..Math.sqrt(c.toDouble()).toLong()).toList().filter { c % it == 0L }

    val disjointSet = mutableSetOf<Long>()

    factors.forEach { commonDiv ->
        if (disjointSet.all { commonDiv % it != 0L }) {
            disjointSet += commonDiv
        }
    }

    println(1 + disjointSet.size)
}

tailrec fun gcd(a: Long, b: Long): Long {
    when (b) {
        0L -> return a
        else -> return gcd(b, a % b)
    }
}