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)

fun main(args: Array<String>) {
    val (a, b) = readLongList()
    val aFactors = primeFactor(a).keys
    val bFactors = primeFactor(b).keys
    println((aFactors.intersect(bFactors)).size + 1)
}

/*!
    O(n^(1/2)) // n * n <= Long.MAX_VALUE n <= 10^8 or more
 */
fun primeFactor(n: Long): Map<Long, Long> {
    val factorMap = mutableMapOf<Long, Long>()
    if (n == 1L) {
        factorMap[n] = 1
        return factorMap
    }

    var target = n
    var i = 2L
    while (i * i <= target) {
        while (target % i == 0L) {
            factorMap[i] = factorMap.getOrElse(i) { 0L } + 1L
            target /= i
        }
        i++
    }

    if (target != 1L) { factorMap[target] = 1 }
    return factorMap
}

fun readInteger() = readLine()!!.toInt()
fun readLong() = readLine()!!.toLong()
fun readStringList() = readLine()!!.split(" ")
fun readIntegerList() = readStringList().map(String::toInt)
fun readLongList() = readStringList().map(String::toLong)