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: Time Limit Exceeded)

import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.NoSuchElementException;


public class Main{
	static FastScanner sc = new FastScanner();
	static PrintWriter out = new PrintWriter(System.out);
	
	public static void main(String[] args) {
		long a = sc.nextLong();
		long b = sc.nextLong();
		
		long num = gcd(a,b);
		long ans = 1;
		
		long i=2; 
		
		if (num==1)
			ans = 1;
		
		else if (num==2 || num==3)
			ans = 2;
		
		else {
			while (i*i<=num){
				if (num%i==0){
					ans++;
					while (num%i==0)
						num/=i;
				}
				i++;
				
				if (isPrime(num, i)) {
					ans++;
					break;
				}	
			}
		}
		
		out.println(ans);
        out.flush();
	}
	
	static long gcd (long a, long b)  { 
        if (a==0)  
            return b; 
        return gcd(b%a,a); 
    } 
	
	static boolean isPrime (long n, long start) {
		if (n==1)
			return false;
        for (long i=start; i*i<= n; i++){
            if (n%i==0){
                return false;
            }
        }
        return true;
	}
	
	static class FastScanner {
	    private final InputStream in = System.in;
	    private final byte[] buffer = new byte[1024];
	    private int ptr = 0;
	    private int buflen = 0;

	    private boolean hasNextByte() {
	      if (ptr < buflen) {
	        return true;
	      } else {
	        ptr = 0;
	        try {
	          buflen = in.read(buffer);
	        } catch (IOException e) {
	          e.printStackTrace();
	        }
	        if (buflen <= 0) {
	          return false;
	        }
	      }
	      return true;
	    }

	    private int readByte() {
	      if (hasNextByte()) return buffer[ptr++];
	      else return -1;
	    }

	    private static boolean isPrintableChar(int c) {
	      return 33 <= c && c <= 126;
	    }

	    private void skipUnprintable() {
	      while (hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++;
	    }

	    public boolean hasNext() {
	      skipUnprintable();
	      return hasNextByte();
	    }

	    public String next() {
	      if (!hasNext()) throw new NoSuchElementException();
	      StringBuilder sb = new StringBuilder();
	      int b = readByte();
	      while (isPrintableChar(b)) {
	        sb.appendCodePoint(b);
	        b = readByte();
	      }
	      return sb.toString();
	    }

	    public long nextLong() {
	      if (!hasNext()) throw new NoSuchElementException();
	      long n = 0;
	      boolean minus = false;
	      int b = readByte();
	      if (b == '-') {
	        minus = true;
	        b = readByte();
	      }
	      if (b < '0' || '9' < b) {
	        throw new NumberFormatException();
	      }
	      while (true) {
	        if ('0' <= b && b <= '9') {
	          n *= 10;
	          n += b - '0';
	        } else if (b == -1 || !isPrintableChar(b)) {
	          return minus ? -n : n;
	        } else {
	          throw new NumberFormatException();
	        }
	        b = readByte();
	      }
	    }

	    public int nextInt() {
	      return (int) nextLong();
	    }

	    public int[] nextIntArray(int N, boolean oneBased) {
	      if (oneBased) {
	        int[] array = new int[N + 1];
	        for (int i = 1; i <= N; i++) {
	          array[i] = sc.nextInt();
	        }
	        return array;
	      } else {
	        int[] array = new int[N];
	        for (int i = 0; i < N; i++) {
	          array[i] = sc.nextInt();
	        }
	        return array;
	      }
	    }

	    public long[] nextLongArray(int N, boolean oneBased) {
	      if (oneBased) {
	        long[] array = new long[N + 1];
	        for (int i = 1; i <= N; i++) {
	          array[i] = sc.nextLong();
	        }
	        return array;
	      } else {
	        long[] array = new long[N];
	        for (int i = 0; i < N; i++) {
	          array[i] = sc.nextLong();
	        }
	        return array;
	      }
	    }
	  }

	}