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.



Sample input:
12 18


Sample output:
3

Submission status: Time Limit Exceeded

Solution code:
# -*- coding: utf-8 -*-
# abc142/abc142_d
import sys

s2nn = lambda s: [int(c) for c in s.split(' ')]
ss2nn = lambda ss: [int(s) for s in list(ss)]
ss2nnn = lambda ss: [s2nn(s) for s in list(ss)]
i2s = lambda: sys.stdin.readline().rstrip()
i2n = lambda: int(i2s())
i2nn = lambda: s2nn(i2s())

prime = 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943231,943249,943273,943277,943289,943301,943303,943307,943321,943343,943357,943363,943367,943373,943387,943403,943409,943421,943429,943471,943477,943499,943511,943541,943543,943567,943571,943589,943601,943603,943637,943651,943693,943699,943729,943741,943751,943757,943763,943769,943777,943781,943783,943799,943801,943819,943837,943841,943843,943849,943871,943903,943909,943913,943931,943951,943967,944003,944017,944029}

def main():
    A, B = i2nn()
    ds = set()
    for i in range(2, int((min(A, B))**1/2) + 1):
        if A % i == 0 and B % i == 0:
            check(i, ds)
    #print(ds)
    print(len(ds)+1)
    return


def check(n, ds):
    if n in prime:
        ds.add(n)
        return
    for d in ds:
        if n % d == 0:
            return
    ds.add(n)
    return

main()