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)

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

val memo = hashMapOf<Int, Long>()
fun generatePrime(index: Int): Long {
    if (index == 0) {
        return 2
    }
    if (index == 1) {
        return 3
    }
    memo[index]?.let {
        return it
    }
    val prev = generatePrime(index - 1)
    var next = prev + 2
    var i = 0
    var prime = 0L
    while (i < index - 1 && next > 2 * prime) {
        prime = generatePrime(++i)
        if (next % prime == 0L) {
            next += 2
            i = 1
        }
    }
    memo[index] = next
    return next
}

fun isPrime(candidate: Long): Boolean {
    var i = 0
    var prime = 0L
    while (candidate > 2 * prime) {
        prime = generatePrime(++i)
        if (candidate % prime == 0L) {
            return false
        }
    }
    return true
}

fun main(args: Array<String>) {
    val (a, b) = readLine()?.split(" ")?.map(String::toLong) ?: return
    var l = gcd(a, b)
    var i = 0
    val primes = mutableSetOf<Long>()
    if (l != 1L && isPrime(l)) {
        println("2")
        return
    }
    var p = 0L
    val e = Math.sqrt(l.toDouble()).toLong()
    while (l != 1L || p < e) {
        p = generatePrime(i)
        while (l % p == 0L) {
            l /= p
            primes.add(p)
        }
        i++
    }
    if (l != 1L) {
        println((primes.size + 2).toString())
    } else {
        println((primes.size + 1).toString())
    }
}