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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.util.*;

@SuppressWarnings("unchecked")
public class Main {
	// public static void printArray(int[] a) {
	// 	for (int i = 0; i < a.length; i++) {
	// 		System.out.print(a[i] + ", ");
	// 	}
	// 	System.out.println();
	// }

	// public static<T> void printArrayT(T[] a) {
	// 	for (int i = 0; i < a.length; i++) {
	// 		System.out.print(a[i] + ", ");
	// 	}
	// 	System.out.println();
	// }

	public static String joinInt(int[] a, String separator) {
		StringBuilder sb = new StringBuilder();
		for (int i = 0; i < a.length; i++) {
			if (i > 0) {
				sb.append(separator);
			}
			sb.append(a[i]);
		}
		return sb.toString();		
	}

	static int[] nextIntArray(Scanner sc, int N) {
		int[] arr = new int[N];
		for (int i = 0; i < N; i++) {
			arr[i] = sc.nextInt();
		}
		return arr;
	}

	public static long gcd(long m, long n) {
		if(m < n) return gcd(n, m);
		if(n == 0) return m;
		return gcd(n, m % n);
	}

	public static boolean[] sieve(int n) {
		boolean[] array = new boolean[n + 2];
		Arrays.fill(array, true);
		array[0] = false;
		array[1] = false;
		for (int i = 2; i*i < array.length; i++) {
			if (!array[i]) continue;
			for (int j = i*i; j < array.length; j += i) {
				array[j] = false;
			}
		}
		return array;
	}

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		long A = sc.nextLong();
		long B = sc.nextLong();
		long gcd = gcd(A, B);
		// System.out.println("gcd =  "+ gcd);
		// int max = (int)Math.sqrt((double)gcd) + 1;
		// boolean[] sieve = sieve(max);
		// int cnt = 1;
		// System.out.println("sqrt =  "+ sqrt);

		int cnt = 1;
		{
			long i;
			for (i = 2; i * i <= gcd; i++) {
				// if (i < sieve.length && sieve[(int)i] == false) continue; // 素数でない
				if (gcd % i == 0) {
					gcd /= i;
					cnt++;
					while (gcd % i == 0) gcd /= i;
				}
			}
			// gcd は素数
			if (cnt > 1) {
				for (; i <= gcd; i++) {
					// if (i < sieve.length && sieve[(int)i] == false) continue; // 素数でない
					if (gcd % i == 0) {
						gcd /= i;
						cnt++;
						while (gcd % i == 0) gcd /= i;
					}
				}	
			}
		}

		System.out.println(cnt);
	}
}