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.*;

public class ModifiedGCD {
    static int[] div;
    static int idx;
    public static int gcd(int a,int b) {
        if(b<a) return gcd(b,a);
        if(a==0) return b;
        return gcd(b%a,a);
    }
    public static int BS(int r) {
        int l=0; int h=idx,mid;
        while(l<h) {
        mid=l+(h-l)/2;
        if(div[mid]<r) l=mid+1;
        else h=mid;
        }
        if(l>=idx||div[l]>r) return l-1;
        return l;
    }
    public static void main(String[] args) {
        Scanner sc=new Scanner(System.in);
        int a=sc.nextInt(),b=sc.nextInt(),l,h,gcd=gcd(a,b);
        int n=sc.nextInt();
        div=new int[(int) (2*Math.sqrt(gcd)+1)+3];
       idx=0;
        for(int i=1;i<=(int)(Math.sqrt(gcd)+1);i++) if(gcd%i==0) {
            div[idx++]=i;
            div[idx++]=gcd/i;
        }
        div[idx++]=gcd;
        Arrays.sort(div,0,idx);
        for(int i=0;i<n;i++) {
            l=sc.nextInt();
            h=sc.nextInt();
            int r=BS(h);
            //System.out.println(gcd+" "+r+" "+div[r]);
            if(div[r]<l) System.out.println(-1);
            else System.out.println(div[r]);
        }
    }
}