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: Runtime Error)

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.math.BigDecimal;
import java.util.HashSet;
import java.util.Set;

public class Main {

	/* several useful subroutines */
	private static BufferedReader brStdin = new BufferedReader(new InputStreamReader(System.in));
	private static String[] readBuf = null;
	private static int readPtr = 0;
	private static String getString() throws IOException {
		while ( readBuf == null || readPtr >= readBuf.length ) {
			readBuf = brStdin.readLine().split(" ");
			readPtr = 0;
		}
		return readBuf[readPtr++];
	}
	private static int getInt() throws IOException {
		return Integer.parseInt(getString());
	}
	private static long getLong() throws IOException {
		return Long.parseLong(getString());
	}
	private static BigDecimal getBD() throws IOException {
		return new BigDecimal(getString());
	}
	@SuppressWarnings("unused")
	private static String[] getStringArray(int size) throws IOException {
		String stringArray[] = new String[size];
		for (int i = 0; i < stringArray.length; i++) {
			stringArray[i] = getString();
		}
		return stringArray;
	}
	@SuppressWarnings("unused")
	private static int[] getIntArray(int size) throws IOException {
		int intArray[] = new int[size];
		for (int i = 0; i < intArray.length; i++) {
			intArray[i] = getInt();
		}
		return intArray;
	}
	@SuppressWarnings("unused")
	private static long[] getLongArray(int size) throws IOException {
		long longArray[] = new long[size];
		for (int i = 0; i < longArray.length; i++) {
			longArray[i] = getLong();
		}
		return longArray;
	}
	@SuppressWarnings("unused")
	private static BigDecimal[] getBDArray(int size) throws IOException {
		BigDecimal bdArray[] = new BigDecimal[size];
		for (int i = 0; i < bdArray.length; i++) {
			bdArray[i] = getBD();
		}
		return bdArray;
	}

	
	/* main routine */
	public static void main(String args[]) throws IOException {
		int a = getInt();
		int b =  getInt();
		if ( a  < b ) {
			int t = a;
			a = b;
			b = t;
		}
		while ( b > 0 ) {
			int t = b;
			b = a % b;
			a = t;
		}
		int cnt = 1;
		for ( int k = 2 ; k <= a ; k+=2 ) {
			if ( a % k == 0 ) {
				cnt++;
				do {
					a /= k;
				} while ( a % k == 0 ) ;
			}
			if ( k == 2 ) {
				k = 1;
			}
		}
		System.out.println(cnt);
	}
}