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.math.BigInteger;

public class hell
{
    public static void main(String args[])
    {
        Scanner cin = new Scanner(System.in);
        int a = cin.nextInt(), b = cin.nextInt();
        TreeSet<Integer> div1 = new TreeSet<Integer>(), div2 = new TreeSet<Integer>();
        for(int i=1; i*i<=a; i++)
        {
            if( a%i == 0 )
            {
                int x = i, y = a/i;
                div1.add(x);
                if( x!=y ) div1.add(y);
            }
        }
        for(int i=1; i*i<=b; i++)
        {
            if( b%i == 0 )
            {
                int x = i, y = b/i;
                div2.add(x);
                if( x!=y ) div2.add(y);
            }
        }
        TreeSet<Integer> common = new TreeSet<Integer>();
        for(int i:div1) if( div2.contains(i) ) common.add(i);
        // for(int i:common) System.out.print(i+" ");
        // System.out.println();
        int[] s = new int[common.size()];
        int it = 0;
        for(int i:common) s[it++] = i;

        int q = cin.nextInt();
        for(int query=0; query<q; query++)
        {
            int l = cin.nextInt(), r = cin.nextInt();
            int LO = 0, HI = common.size() - 1, ans = -1;
            while( LO<=HI )
            {
                int M = (LO+HI) >> 1;
                if( s[M] > r ) HI = M-1;
                else
                {
                    ans = Math.max( ans,s[M] );
                    LO = M+1;
                }
            }
            if( ans < l ) System.out.println(-1);
            else System.out.println(ans);
        }
    }
}