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 (GCC 5.4.1) (judge verdict: Accepted)

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <math.h>

int X[100], Y[100];


// 最大公約数を求める
long long int GCD (long long int a, long long int b) {
    long long int tmp, x, r;
    if (a<b) {
        tmp = a;
        a = b;
        b = tmp;
    }
    r = a % b;
    while (r!=0) {
      a = b;
      b = r;
      r = a % b;
    }
    return b;
}


int main() {
  long long A, B, G, result;
  int i;
  scanf ("%lld %lld", &A, &B);
  
  G = GCD(A,B);
//  printf("G=%lld\n",G);
  result = 1;
  for (i=2;i<=sqrt(G);i++) {
     if (G%i==0) result++;
     while (G%i==0) {G/=i;}
  }
  
  if (G!=1) result++;
  
  printf("%lld", result);
  return 0;
}