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.util.*;
import java.lang.*;
import java.io.*;
import java.math.*;
//BigInteger A;
//A= BigInteger.valueOf(54);
//ArrayList<Integer> a=new ArrayList<>();
//TreeSet<Integer> ts=new TreeSet<>();
//HashMap<Integer,Integer> hm=new HashMap<>();
//PriorityQueue<Integer> pq=new PriorityQueue<>();
public final class Codeforces
{
    public static int gcd(int a,int b)
    {
        if(b==0)
        return a;
        return gcd(b,a%b);
    }
    public static void main(String[]args)throws IOException
    {
        int K=(int)Math.pow(10,9)+7;
        FastReader ob=new FastReader();
        //int t=ob.nextInt();
        //while(t-->0)
        {
            int a=ob.nextInt();
            int b=ob.nextInt();
            int g=gcd(a,b);
            ArrayList<Integer> factors=new ArrayList<>();
            for(int i=1;i*i<=g;i++)
            {
                if(g%i==0)
                {
                    factors.add(i);
                    factors.add(g/i);
                }
            }
            Collections.sort(factors);
            int n=ob.nextInt();
            while(n-->0)
            {
                int l=ob.nextInt();
                int h=ob.nextInt();
                int x=Collections.binarySearch(factors,h);
                if(x>=0)
                {
                    int num=factors.get(x);
                    if(num>=l)
                    System.out.println(num);
                    else
                    System.out.println("-1");
                }
                else
                {
                    x=-x-1;
                    int num=factors.get(x-1);
                    if(num>=l)
                    System.out.println(num);
                    else
                    System.out.println("-1");
                }
            }
        }
    }
}
class FastReader {
    BufferedReader br;
    StringTokenizer st;
    public FastReader() {
        br = new BufferedReader(new InputStreamReader(System.in));
    }

    public String next() {
        while (st == null || !st.hasMoreElements()) {
            try {
                st = new StringTokenizer(br.readLine());
            } catch (IOException e)  {
                e.printStackTrace();
            }
        }
        return st.nextToken();
    }
    public String nextLine()
    {
        String s="";
        try {
        s=br.readLine();
        } catch (IOException e)  {
                e.printStackTrace();
            }
        return s;
    }
    public int nextInt() {
        return Integer.parseInt(next());
    }
    public long nextLong() {
        return Long.parseLong(next());
    }
    public double nextDouble() {
        return Double.parseDouble(next());
    }
}