Alice gave Bob two integers a and b (a > 0 and b ≥ 0). Being a curious boy, Bob wrote down an array of non-negative integers with \operatorname{MEX} value of all elements equal to a and \operatorname{XOR} value of all elements equal to b.

What is the shortest possible length of the array Bob wrote?

Recall that the \operatorname{MEX} (Minimum EXcluded) of an array is the minimum non-negative integer that does not belong to the array and the \operatorname{XOR} of an array is the [bitwise XOR](https://en.wikipedia.org/wiki/Bitwise_operation#XOR) of all the elements of the array.

Input

The input consists of multiple test cases. The first line contains an integer t (1 ≤ t ≤ 5 ⋅ 10^4) — the number of test cases. The description of the test cases follows.

The only line of each test case contains two integers a and b (1 ≤ a ≤ 3 ⋅ 10^5; 0 ≤ b ≤ 3 ⋅ 10^5) — the \operatorname{MEX} and \operatorname{XOR} of the array, respectively.

Output

For each test case, output one (positive) integer — the length of the shortest array with \operatorname{MEX} a and \operatorname{XOR} b. We can show that such an array always exists.

Example

Input


5
1 1
2 1
2 0
1 10000
2 10000


Output


3
2
3
2
3

Note

In the first test case, one of the shortest arrays with \operatorname{MEX} 1 and \operatorname{XOR} 1 is [0, 2020, 2021].

In the second test case, one of the shortest arrays with \operatorname{MEX} 2 and \operatorname{XOR} 1 is [0, 1].

It can be shown that these arrays are the shortest arrays possible.

import java.io.*;
import java.util.*;
 
public class Prime {
    static FastReader s=new FastReader();
    static PrintWriter out=new PrintWriter(System.out);
    public static int I(){return s.I();}
    public static long L(){return s.L();}
    public static double D(){return s.D();}
    public static String S(){return s.S();}
    static class FastReader { 
 
        BufferedReader br; 
 
        StringTokenizer st; 
 
 
 
        public FastReader() 
 
        { 
 
            br = new BufferedReader( 
 
                new InputStreamReader(System.in)); 
 
        } 
 
 
 
        String next() 
 
        { 
 
           while (st == null || !st.hasMoreElements()) { 
 
               try { 
 
                   st = new StringTokenizer(br.readLine()); 
 
                } 
 
                catch (IOException e) { 
 
                    e.printStackTrace(); 
 
                } 
 
            } 
 
            return st.nextToken(); 
 
        } 
 
 
 
        int I() { return Integer.parseInt(next()); } 
 
 
 
        long L() { return Long.parseLong(next()); } 
 
 
 
        double D() 
 
        { 
 
           return Double.parseDouble(next()); 
 
        } 
 
 
 
        String S() 
 
        { 
 
            String str = ""; 
 
            try { 
 
               str = br.readLine(); 
 
            } 
 
            catch (IOException e) { 
 
             e.printStackTrace(); 
 
            } 
 
            return str; 
 
        } 
 
    } 
 
    public static void main(String[] args)
    {
        int t=I();
        while(t--!=0){
            int a=I();
            int b=I();
            int xor=0;
            int num=a-1;
            if(num%4==0)xor=num;
            else if(num%4==1)xor=1;
            else if(num%4==2)xor=num+1;
            else if(num%4==3)xor=0;
            
            if(xor==b)System.out.println (a);
            else if((xor^b)==b)System.out.println (a+1);
            else System.out.println(a+2);
        }
        out.close();
	}
}