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.*;
  import java.util.*;
  
  public class B {
      static FastReader reader = new FastReader();
      static OutputWriter out = new OutputWriter(System.out);
  
      public static void main(String[] args) {
          int tests = reader.nextInt();
  
          int[] xors = new int[(int) (3e5+10)];
          xors[0] = 0;
          for (int i = 1; i < xors.length; i++) {
              xors[i] = xors[i-1] ^ i;
          }
          for(int test = 1; test <= tests; test++) {
              int mex = reader.nextInt();
              int resXor = reader.nextInt();
              // 0 ... mex - 1
              int result = mex;
              int curXor = xors[mex-1];
              if (curXor == resXor) {
                  out.println(result);continue;
              }
  
              int toAdd = curXor ^ resXor;
              if (toAdd == mex) {
                  out.println(result + 2);
              } else {
                  out.println(result + 1);
              }
  
          }
          out.flush();
      }
  
      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 nextInt() {
              return Integer.parseInt(next());
          }
  
          long nextLong() {
              return Long.parseLong(next());
          }
  
          double nextDouble() {
              return Double.parseDouble(next());
          }
  
          String nextLine() {
              String str = "";
              try {
                  str = br.readLine();
              } catch (IOException e) {
                  e.printStackTrace();
              }
              return str;
          }
      }
  
      public static class OutputWriter {
          private final PrintWriter writer;
  
          public OutputWriter(OutputStream outputStream) {
              writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
          }
  
          public OutputWriter(Writer writer) {
              this.writer = new PrintWriter(writer);
          }
  
          public void print(char[] array) {
              writer.print(array);
          }
  
          public void print(Object... objects) {
              for (int i = 0; i < objects.length; i++) {
                  if (i != 0) {
                      writer.print(' ');
                  }
                  writer.print(objects[i]);
              }
          }
  
          public void print(int[] array) {
              for (int i = 0; i < array.length; i++) {
                  if (i != 0) {
                      writer.print(' ');
                  }
                  writer.print(array[i]);
              }
          }
  
          public void print(double[] array) {
              for (int i = 0; i < array.length; i++) {
                  if (i != 0) {
                      writer.print(' ');
                  }
                  writer.print(array[i]);
              }
          }
  
          public void print(long[] array) {
              for (int i = 0; i < array.length; i++) {
                  if (i != 0) {
                      writer.print(' ');
                  }
                  writer.print(array[i]);
              }
          }
  
          public void println(int[] array) {
              print(array);
              writer.println();
          }
  
          public void println(double[] array) {
              print(array);
              writer.println();
          }
  
          public void println(long[] array) {
              print(array);
              writer.println();
          }
  
          public void println() {
              writer.println();
          }
  
          public void println(Object... objects) {
              print(objects);
              writer.println();
          }
  
          public void print(char i) {
              writer.print(i);
          }
  
          public void println(char i) {
              writer.println(i);
          }
  
          public void println(char[] array) {
              writer.println(array);
          }
  
          public void printf(String format, Object... objects) {
              writer.printf(format, objects);
          }
  
          public void close() {
              writer.close();
          }
  
          public void flush() {
              writer.flush();
          }
  
          public void print(long i) {
              writer.print(i);
          }
  
          public void println(long i) {
              writer.println(i);
          }
  
          public void print(int i) {
              writer.print(i);
          }
  
          public void println(int i) {
              writer.println(i);
          }
  
          public void separateLines(int[] array) {
              for (int i : array) {
                  println(i);
              }
          }
      }
  }