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: Accepted)

#include <cstdio>
#include <cctype>
#define int long long
#define il inline
#define rgi register long long
#define sp putchar(' ')
#define el putchar('\n')
using namespace std;
il int ri()
{
	register int o1=0;
	register bool o2=0;
	register char o3;
	while(!isdigit(o3=getchar()))
		o2|=o3=='-';
	while(isdigit(o3))
		o1=(o1<<1)+(o1<<3)+(o3^48),o3=getchar();
	return o2?-o1:o1;
}
il void wi(int o1)
{
	if(o1<0)
		putchar('-'),o1=-o1;
	rgi o2=o1/10;
	if(o2)
		wi(o2);
	putchar((o1-(o2<<1)-(o2<<3))^48);
}
int a,b,c;
il int gcd(int p,int q)
{
	if(q==0)
		return p;
	return gcd(q,p%q);
}
il int divide(int n)
{
	int ret=0;
	for(rgi i=2;i*i<=n;++i)
		if(n%i==0)
		{
			++ret;
			while(n%i==0)
				n/=i;
		}
	if(n>1)
		++ret;
	return ret+1;
}
signed main()
{
	a=ri(),b=ri();
	c=gcd(a,b);
	int ans=divide(c);
	wi(ans);
	return 0;
}