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:
//package NumberTheory;

import java.io.*;
import java.util.ArrayList;
import java.util.Collections;
import java.util.StringTokenizer;
public class ModifiedGCD {
    public static void main(String[] args) throws IOException, InterruptedException {
        Scanner sc = new Scanner(System.in);
        PrintWriter pw = new PrintWriter(System.out);
        int a=sc.nextInt();
        int b=sc.nextInt();
        int gcd=gcd(a,b);
        ArrayList<Integer> list = new ArrayList<>();
        for(int i=1;i*i<=gcd;i++)
        	if(gcd%i==0) {
        		list.add(i);
        		if(gcd/i!=i)
        			list.add(gcd/i);
        	}
        Collections.sort(list);
        int t=sc.nextInt();
        while(t-->0) {
        	int l=sc.nextInt();
        	int h=sc.nextInt();
        	int lo=0;
        	int hi=list.size()-1;
        	int ans=-1;
        	while(lo<=hi) {
        		int mid=(lo+hi)/2;
        		if(list.get(mid)<=h) {
        			ans=list.get(mid);
        			lo=mid+1;
        		}
        		else
        			hi=mid-1;
        	}
        	pw.println(ans<l?-1:ans);
        }
        pw.flush();
    }
    static int gcd(int a, int b) {
    	return b==0?a:gcd(b,a%b);
    }
 
    static class Scanner
    {
        StringTokenizer st;
        BufferedReader br;
 
        public Scanner(InputStream system) {br = new BufferedReader(new InputStreamReader(system));}
        public String next() throws IOException
        {
            while (st == null || !st.hasMoreTokens())
                st = new StringTokenizer(br.readLine());
            return st.nextToken();
        }
        public String nextLine()throws IOException{return br.readLine();}
        public int nextInt() throws IOException {return Integer.parseInt(next());}
        public double nextDouble() throws IOException {return Double.parseDouble(next());}
        public char nextChar()throws IOException{return next().charAt(0);}
        public Long nextLong()throws IOException{return Long.parseLong(next());}
        public boolean ready() throws IOException{return br.ready();}
        public void waitForInput() throws InterruptedException {Thread.sleep(4000);}
    }
 }