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)

import java.util.*

fun main(args : Array<String>) {
    val scanner = Scanner(System.`in`)
    val a = scanner.nextLong()
    val b = scanner.nextLong()
    val gcd = if (a > b) gcd(a, b) else gcd(b, a)
    val primeList = getPrimeList(gcd)
    var result = 1
    if (primeList.isNotEmpty()) {
        for (i in 0..primeList.size-1) {
            if (gcd % primeList[i] == 0L) result += 1
        }
    }
    println(result)
}

tailrec fun gcd(large: Long, small: Long): Long {
    if (small == 0L) return large
    return gcd(small, large % small)
}

fun getPrimeList(n: Long): List<Long> {
    if (n < 2) return emptyList()
    val primeList = mutableListOf<Long>()
    val searchList = (2..n).toMutableList()

    do {
        val currentNum = searchList.first()
        primeList.add(currentNum)
        searchList.removeAll { it % currentNum == 0L }
    } while (n > currentNum * currentNum)

    return primeList.plus(searchList)
}