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 C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

/***********************************************
 *                   _ooOoo_                   *
 *                  o8888888o                  *
 *                  88" . "88                  *
 *                  (| -_- |)                  *
 *                  O\  =  /O                  *
 *               ____/`---'\____               *
 *             .'  \\|     |//  `.             *
 *            /  \\|||  :  |||//  \            *
 *           /  _||||| -:- |||||-  \           *
 *           |   | \\\  -   * |    |           *
 *           | \_|  ''\---/''  |   |           *
 *           \  .-\__  `-`  ___/-. /           *
 *         ___`. .'  /--.--\  `. . __          *
 *      ."" '<  `.___\_<|>_/___.'  >'"".       *
 *     | | :  `- \`.;`\ _ /`;.`/ - ` : | |     *
 *     \  \ `-.   \_ __\ /__ _/   .-` /  /     *
 *======`-.____`-.___\_____/___.-`____.-'======*
 *                   `=---='                   *
 *^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

             佛祖保佑       永无BUG

   本程序已经经过开光处理，绝无可能再产生bug
 **********************************************/
#include <cmath>
#include <ctime>
#include <cstdio>
#include <cstring>
#include <iostream>
#include <algorithm>
using namespace std;

#define ll long long
#define db1(x) cout<<#x<<"="<<(x)<<endl
#define db2(x,y) cout<<#x<<"="<<(x)<<", "<<#y<<"="<<(y)<<endl
#define db3(x,y,z) cout<<#x<<"="<<(x)<<", "<<#y<<"="<<(y)<<", "<<#z<<"="<<(z)<<endl

bool num[3000010]={1,1};
ll prime[3000100];

ll gcd(ll a,ll b)
{
    if(b==0)return a;
    else return gcd(b,a%b);
}

ll getprime()
{
    for(int i=2;i*i<=3000000;i++)
        if(!num[i])
            for(int j=i;j*i<=3000000;j++)
                num[i*j]=true;
    
    int k=0;
    for(int i=2;i<=3000000;i++)
    {
        if(!num[i])prime[k++]=i;
    }

    for(int i=0;i<k;i++)
        if(prime[i]==0)
        {
            printf("k=%lld\n",k);break;
        }

    return k;
}

int main(void)
{
    #ifdef test
    freopen("in.txt","r",stdin);
    //freopen("in.txt","w",stdout);
    clock_t start=clock();
    #endif //test

    ll a,b,g=0,k=getprime(),sum=1;
    scanf("%lld%lld",&a,&b);
    g=gcd(a,b);

    for(int i=0;i<k;i++)
    {
        if(prime[i]*prime[i]>g)break;

        if(g%prime[i]==0)
        {
            sum++;
            while(g%prime[i]==0)g/=prime[i];
        }
    }
    printf("%lld\n",sum);


    #ifdef test
    clockid_t end=clock();
    double endtime=(double)(end-start)/CLOCKS_PER_SEC;
    printf("\n\n");
    cout<<"Total time:"<<endtime<<"s"<<endl;        //s为单位
    cout<<"Total time:"<<endtime*1000<<"ms"<<endl;    //ms为单位
    #endif //test
    return 0;
}


// ━━━━━━神兽出没━━━━━━
//      ┏┓       ┏┓
//     ┏┛┻━━━━━━━┛┻┓
//     ┃           ┃
//     ┃     ━     ┃
//     ????━????   ┃
//     ┃           ┃
//     ┃    ┻      ┃
//     ┃           ┃
//     ┗━┓       ┏━┛
//       ┃       ┃
//       ┃       ┃
//       ┃       ┗━━━┓
//       ┃           ┣┓
//       ┃           ┏┛
//       ┗┓┓┏━━━━━┳┓┏┛
//        ┃┫┫     ┃┫┫
//        ┗┻┛     ┗┻┛
//
// ━━━━━━感觉萌萌哒━━━━━━