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.text.*;
import java.io.*;

public class Cf75C implements Runnable {
     Set< Integer > divisors = new TreeSet< Integer >( );
     
     public int gcd( int a, int b ) {
         while ( b != 0 ) {
             int t = b;
             b = a % b;
             a = t;
         }

         return a;
     }

     public void solve( ) throws Throwable {
          int low = nextInt( );
          int high = nextInt( );
          int gcd = gcd( low, high );
          for ( int i = 1; i * i <= gcd; ++i ) {
              if ( gcd % i == 0 ) {
                  divisors.add( i );
                  divisors.add( gcd / i );
              }
          }

          //System.err.println( Arrays.toString( divisors.toArray( ) ) );
          final Integer allDivisors[ ] = divisors.toArray( new Integer[ 0 ] );
          int numQueries = nextInt( );
nextQuery:while ( numQueries --> 0 ) {
              low = nextInt( );
              high = nextInt( );
              for ( int i = allDivisors.length - 1; i >= 0; --i ) {
                  if ( low <= allDivisors[ i ] && allDivisors[ i ] <= high ) {
                       out.println( allDivisors[ i ] );
                       continue nextQuery;
                  }

                  
              }
              out.println( -1 );
              
          }

     }

     public void findGCD( ) {
         
     }

     
     public void run( ) {
         try {
             solve( );
             out.close( );
         } catch( Throwable e ) {
             e.printStackTrace( );
         }
     }


     public static void main( String[ ] args ) {
         new Thread( new Cf75C( ) ).start( );
     }

     BufferedReader bIn = new BufferedReader( new InputStreamReader( System.in ) );
     PrintWriter out = new PrintWriter( new PrintStream( System.out ), true );
     StringTokenizer st = new StringTokenizer( "" );

     
     private void split( String s ) {
         st = new StringTokenizer( s );
     }

     private int nextInt( ) throws Throwable {
         return Integer.parseInt( next( ) );
     }

     private double nextDouble( ) throws Throwable {
         return Double.parseDouble( next( ) );
     }
     
     private long nextLong( ) throws Throwable {
         return Long.parseLong( next( ) );
     }

     private String next( ) throws Throwable {
         while ( !st.hasMoreTokens( ) ) {
             String l = bIn.readLine( );
             if ( l == null ) {
                 return null;
             }
             split( l );

         }

         return st.nextToken( );
     }
     
     private String nextLine( ) throws Throwable {
         st = new StringTokenizer( "" );
         return bIn.readLine( );
     }

     private boolean isEOF( ) throws Throwable {
         while ( !st.hasMoreTokens( ) ) {
              String s = bIn.readLine( );
              if ( s == null ) return true;
              split( s );
         }

         return false;
     }


}