description: 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.
solution: 
  import java.io.BufferedReader;
  import java.io.IOException;
  import java.io.InputStreamReader;
  import java.io.OutputStreamWriter;
  import java.io.PrintWriter;
  import java.util.StringTokenizer;
  
  public class MexOr {
  	static PrintWriter pw = new PrintWriter(new OutputStreamWriter(System.out));
  	
  	public static void main(String[] args) {
  		int[] xor_prefix = new int[1_000_000];
  		for(int i = 1; i < xor_prefix.length; i++)
  		{
  			xor_prefix[i] = xor_prefix[i-1]^i;
  		}
  		int t = nextInt();
  		while (t-- != 0) {
  			int a = nextInt(), b = nextInt();
  			int needed = xor_prefix[a-1] ^ b;
  			if(needed == 0)
  				pw.println(a);
  			else if(needed == a)
  				pw.println(a+2);
  			else {
  				pw.println(a+1);
  			}
  			
  		}
  		pw.flush();
  		pw.close();
  	}
  	static StringTokenizer st;
  	static BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
   
  	public static String nextLine() {
  		String s = "";
  		try {
  			s = br.readLine();
  		} catch (IOException e) {
  			// TODO Auto-generated catch block
  			e.printStackTrace();
  		}
  		return s;
  	}
   
  	public static String next() {
  		while (st == null || !st.hasMoreElements()) {
  			try {
  				st = new StringTokenizer(br.readLine());
  			} catch (IOException e) {
  				e.printStackTrace();
  			}
  		}
  		return st.nextToken();
  	}
   
  	public static int nextInt() {
  		return Integer.parseInt(next());
  	}
  	public static long nextLong() {
  		return Long.parseLong(next());
  	}
  }
  