Problem: Well, here is another math class task. In mathematics, GCD is the greatest common divisor, and it's an easy task to calculate the GCD between two positive integers.

A common divisor for two positive numbers is a number which both numbers are divisible by.

But your teacher wants to give you a harder task, in this task you have to find the greatest common divisor d between two integers a and b that is in a given range from low to high (inclusive), i.e. low ≤ d ≤ high. It is possible that there is no common divisor in the given range.

You will be given the two integers a and b, then n queries. Each query is a range from low to high and you have to answer each query.

Input

The first line contains two integers a and b, the two integers as described above (1 ≤ a, b ≤ 109). The second line contains one integer n, the number of queries (1 ≤ n ≤ 104). Then n lines follow, each line contains one query consisting of two integers, low and high (1 ≤ low ≤ high ≤ 109).

Output

Print n lines. The i-th of them should contain the result of the i-th query in the input. If there is no common divisor in the given range for any query, you should print -1 as a result for this query.

Examples

Input

9 27
3
1 5
10 11
9 11


Output

3
-1
9

Solution (in JAVA):

Solution:
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.TreeSet;

public class Main{

	public static void main(String[] args) throws IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		long a, b, v;
	    int n;
	    long l, h, c = 0;
	    TreeSet<Long> div = new TreeSet<Long>();
	    String line = br.readLine();
	    String[] tok = line.split(" ");
	    a = Integer.parseInt(tok[0]);
	    b = Integer.parseInt(tok[1]);
	    v = gcd(a,b);
	    for(int k = 1; k * k <= v; k++){
	    	if(v % k == 0){
	    		div.add(new Long(k));
	    		div.add(new Long(v / k));
	    	}
	    }
	    div.add(v);
	    n = Integer.parseInt(br.readLine());
	    for(int i = 0; i < n; i++){
	    	line = br.readLine();
		    tok = line.split(" ");
		    l = Integer.parseInt(tok[0]);
		    h = Integer.parseInt(tok[1]);
		    c = div.floor(new Long(h));
		    if(c>=l)
			  System.out.println(c);
		    else
		    	System.out.println("-1");
		    c = 0;
	    }
	}

	static long gcd(long x, long y){
	     if(y==0)
	             return x;
	     else
	         return gcd(y,x%y);
	}
	
}