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:
/*
 * To change this license header, choose License Headers in Project Properties.
 * To change this template file, choose Tools | Templates
 * and open the template in the editor.
 */





//import com.sun.xml.internal.ws.util.StringUtils;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.lang.reflect.Array;
import java.math.BigInteger;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.HashSet;
import java.util.List;
import java.util.Scanner;
import java.util.Set;
import java.util.Vector;
import java.util.stream.Collectors;





/**
 *
 * @author george
 */

public class main {
    /*
public static boolean isPrime(long n) {
    if(n < 2) return false;
    if(n == 2 || n == 3) return true;
    if(n%2 == 0 || n%3 == 0) return false;
    long sqrtN = (long)Math.sqrt(n)+1;
    for(long i = 6L; i <= sqrtN; i += 6) {
        if(n%(i-1) == 0 || n%(i+1) == 0) return false;
    }
    return true;
}*/
/*
    private static long f(long l) {
        throw new UnsupportedOperationException("Not supported yet."); //To change body of generated methods, choose Tools | Templates.
    }

public static boolean contains(final int[] arr, final int key) {
    return Arrays.stream(arr).anyMatch(i -> i == key);
}
 static boolean isSubSequence(String str1, String str2, int m, int n)
    {
       
        if (m == 0) 
            return true;
        if (n == 0) 
            return false;
             
        
        if (str1.charAt(m-1) == str2.charAt(n-1))
            return isSubSequence(str1, str2, m-1, n-1);
 
        
        return isSubSequence(str1, str2, m, n-1);
    }

    static int gcdThing(int a, int b) {
    BigInteger b1 = BigInteger.valueOf(a);
    BigInteger b2 = BigInteger.valueOf(b);
    BigInteger gcd = b1.gcd(b2);
    return gcd.intValue();
}
    public static boolean checkAnagram(String str1, String str2) {
        int i=0;
        for (char c : str1.toCharArray()) {
        i = str2.indexOf(c, i) + 1;
        if (i <= 0) { return false; }
    }
    return true;

}
    
    public static Set primeFactors(int num)
    {
        Set<Integer>Prime=new HashSet<Integer>();
        // Print the number of 2s that divide n
        int tw=2;
        while (num%2==0)
        {
            Prime.add(tw);
            num /= 2;
        }
 
        // n must be odd at this point.  So we can
        // skip one element (Note i = i +2)
        for (int i = 3; i <= Math.sqrt(num); i+= 2)
        {
            // While i divides n, print i and divide n
            while (num%i == 0)
            {
                Prime.add(i);
                num/= i;
            }
        }
 
        // This condition is to handle the case whien
        // n is a prime number greater than 2
        if (num> 2)
            Prime.add(num);        
        return Prime;
    }
    public static String Winner(int [] arr)
    {
        int maxsum=-1;
        int temp=0;
        List<Integer> L=Arrays.stream(arr).boxed().collect(Collectors.toList());
        int count=0;
        String winner="First";
        while(L.isEmpty()!=true){
           if(count%2==0){winner="First";
           //take max odd interval
            for (int i = 0; i < L.size(); i++) {
                
            }
            }
           else{winner="Second";
           
           
           
           
           
           
           
           }
           count++;
        }
    
    
    return winner;
    }
    public static String changeCharInPosition(int position, char ch, String str){
    char[] charArray = str.toCharArray();
    charArray[position] = ch;
    return new String(charArray);
    }
    public static boolean CheckCanObtainYfromX(String y,String x){
        boolean cond=true;
        String help="";
        for (int i = 0; i < y.length(); i++) {
            help="";help+=y.charAt(i);
            if(y.contains(help)==false){x=x.replaceFirst(help,"A");cond=false;break;}
            
        }
        return cond;
    }
   public static int LongestPalindrome(String x){
    int n=x.length();
    boolean table[][] = new boolean[n][n];
    int maxLength = 1;
     for (int i = 0; i < n; ++i)
            table[i][i] = true;
   int start = 0;
    for (int i = 0; i < n - 1; ++i) {
            if (x.charAt(i) == x.charAt(i + 1)) {
                table[i][i + 1] = true;
                start = i;
                maxLength = 2;
            }
        }
     for (int k = 3; k <= n; ++k) {
            for (int i = 0; i < n - k + 1; ++i) 
            {
                int j = i + k - 1;
               if (table[i + 1][j - 1] && x.charAt(i) == x.charAt(j)) {
                    table[i][j] = true;
                if (k > maxLength) {
                        start = i;
                        maxLength = k;
                    }
                }
            }
     }
   return maxLength;
   }
   public static long choose(long total, long choose){
    if(total < choose)
        return 0;
    if(choose == 0 || choose == total)
        return 1;
    return choose(total-1,choose-1)+choose(total-1,choose);
}
    public static long bitwiseAdd(int n1, int n2) {
        int x = n1, y = n2;
        int xor, and, temp;
        and = x & y;
        xor = x ^ y;

        while (and != 0) {
            and <<= 1;
            temp = xor ^ and;
            and &= xor;
            xor = temp;
        }
        return (xor%2);
    }
    public static boolean compare(String a,String b){
        for (int i = 0; i < a.length(); i++) {
            if(a.charAt(i)!=b.charAt(i)&&a.charAt(i)!='?'){return false;}
        }
  return true;
    }*/
/*public static boolean isUniqueChars(String str) {
    // short circuit - supposed to imply that
    // there are no more than 256 different characters.
    // this is broken, because in Java, char's are Unicode,
    // and 2-byte values so there are 32768 values
    // (or so - technically not all 32768 are valid chars)
    if (str.length() > 256) {
        return false;
    }
    // checker is used as a bitmap to indicate which characters
    // have been seen already
    int checker = 0;
    for (int i = 0; i < str.length(); i++) {
        // set val to be the difference between the char at i and 'a'
        // unicode 'a' is 97
        // if you have an upper-case letter e.g. 'A' you will get a
        // negative 'val' which is illegal
        int val = str.charAt(i) - 'a';
        // if this lowercase letter has been seen before, then
        // the corresponding bit in checker will have been set and
        // we can exit immediately.
        if ((checker & (1 << val)) > 0) return false;
        // set the bit to indicate we have now seen the letter.
        checker |= (1 << val);
    }
    // none of the characters has been seen more than once.
    return true;
}*/
 /*private static int [] PossibilitiesAsBinaryTruthTable(int n) {
        int rows = (int) Math.pow(2,n);
        int [] possibleTrack=new int[rows];
        int trackPerRow;
        for (int i=0; i<rows; i++) {
            trackPerRow=0;
            for (int j=n-1; j>=0; j--) {
                if(((i/(int) Math.pow(2, j))%2)==0){trackPerRow--;}
                else if(((i/(int) Math.pow(2, j))%2)==1){trackPerRow++;}
            }
            possibleTrack[i]=trackPerRow;
        }
        return possibleTrack;
    }
    //Steins GCD Algo
     public static long gcd(long u, long v)
    {
        long shift;
        if (u == 0)
            return v;
        if (v == 0)
            return u;
        for (shift = 0; ((u | v) & 1) == 0; ++shift) 
        {
            u >>= 1;
            v >>= 1;
        }
        while ((u & 1) == 0)
            u >>= 1;
        do 
        {
            while ((v & 1) == 0)  
                v >>= 1;
 
            if (u > v) 
            {
                long t = v; 
                v = u; 
                u = t;
            }  
            v = v - u;                      
        } while (v != 0);
 
        return u << shift; 
    }*/
     public static long gcd(long p, long q) {
        if (q == 0) return p;
        else return gcd(q, p % q);
    }
    public static void main (String []  args) throws IOException 
    {
        Scanner s=new Scanner(System.in);
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
        PrintWriter pw=new PrintWriter(new OutputStreamWriter(System.out));
        String line=br.readLine();
        String [] ab=line.split(" ");
        long a=Long.parseLong(ab[0]);
        long b=Long.parseLong(ab[1]);
        int n=Integer.parseInt(br.readLine());
         String [] vecsS=new String[n];
        for (int i = 0; i < n; i++) {
            vecsS[i]=br.readLine();
        }
        String [] help=new String[2];
        int [] x=new int[n];int []y=new int[n];
        for (int i = 0; i < n; i++) {
            help=vecsS[i].split(" ");
            x[i]=Integer.parseInt(help[0]);
            y[i]=Integer.parseInt(help[1]);
           }
       /* BigInteger A=new BigInteger(String.valueOf(a));
        BigInteger B=new BigInteger(String.valueOf(b));*/
        long gcd=gcd(a, b);
        Vector<Long>Divisors=new Vector<>();
        for (long i = 1; i <=Math.sqrt(gcd); i++) {
            if(gcd%i==0){Divisors.add(i);if(gcd/i!=i)Divisors.add(gcd/i);}
        }
        long[] Divarray = Divisors.stream().mapToLong(i->i).toArray();
        Arrays.sort(Divarray);
        if(Divarray.length==1){
        long compare=Divarray[0];
            for (int i = 0; i < n; i++) {
                if(compare>=x[i]&&compare<=y[i]){System.out.println(compare);}
                else{System.out.println(-1);}
            }
        
        }
        else{
        for (int i = 0; i < n; i++) {
            if(x[i]>Divarray[Divarray.length-1]){System.out.println(-1);}
            else{
                long tempa=-1;long tempb=-1;long temp=-1;long max=-1;
                //fatest way by usinng BNS
                for (int j = 0; j <=Divarray.length/2; j++) {
                    if(Divarray[j]>=x[i]&&Divarray[j]<=y[i]){tempa=Divarray[j];}
                    if(Divarray[Divarray.length-(j+1)]>=x[i]&&Divarray[Divarray.length-(j+1)]<=y[i]){tempb=Divarray[Divarray.length-(j+1)];}
                    temp=Math.max(tempa, tempb);
                    if(temp>max){max=temp;}
                }
                System.out.println(max);
            }
        }
        }
        
    }  
   }