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 test {
    //--------------------------INPUT READER--------------------------------//
    static class fs {
        public BufferedReader br;
        StringTokenizer st = new StringTokenizer("");

        public fs() { this(System.in); }
        public fs(InputStream is) {
            br = new BufferedReader(new InputStreamReader(is));
        }
        String next() {
            while (!st.hasMoreTokens()) {
                try { st = new StringTokenizer(br.readLine()); }
                catch (IOException e) { e.printStackTrace(); }
            }
            return st.nextToken();
        }

        int ni() { return Integer.parseInt(next()); }
        long nl() { return Long.parseLong(next()); }
        double nd() { return Double.parseDouble(next()); }
        String ns() { return next(); }

        int[] na(int n) {
            int[] a = new int[n];
            for (int i = 0; i < n; i++) a[i] = ni();
            return a;
        }
    }
    //-----------------------------------------------------------------------//

    //---------------------------PRINTER-------------------------------------//
    static class Printer {
        static PrintWriter w;
        public Printer() {this(System.out);}
        public Printer(OutputStream os) {
            w = new PrintWriter(os);
        }
        public void p(int i) {w.println(i);};
        public void p(long l) {w.println(l);};
        public void p(double d) {w.println(d);};
        public void p(String s) { w.println(s);};
        public void pr(int i) {w.println(i);};
        public void pr(long l) {w.print(l);};
        public void pr(double d) {w.print(d);};
        public void pr(String s) { w.print(s);};
        public void pl() {w.println();};
        public void close() {w.close();};
    }
    //------------------------------------------------------------------------//

    //--------------------------VARIABLES------------------------------------//
    static fs sc = new fs();
    static OutputStream outputStream = System.out;
    static Printer w = new Printer(outputStream);
    //-----------------------------------------------------------------------//

    //--------------------------ADMIN_MODE-----------------------------------//
    private static void ADMIN_MODE() throws IOException {
        if (System.getProperty("ONLINE_JUDGE") == null) {
            w = new Printer(new FileOutputStream("output.txt"));
            sc = new fs(new FileInputStream("input.txt"));
        }
    }
    //-----------------------------------------------------------------------//

    static int[] pre;
    //----------------------------START--------------------------------------//
    public static void main(String[] args)
            throws IOException {

        ADMIN_MODE();

        pre = new int[1000000];
        for(int i = 1; i < 1000000; i++) {
            pre[i] = i^pre[i-1];
        }

        int t = sc.ni();
        while(t-->0)
            solve();


        w.close();
    }

    static void solve() throws IOException {
        int a = sc.ni();
        int b = sc.ni();
        int res = 0;
        res = pre[a-1];
        if(res == b) {
            w.p(a);
        } else {
            int need = res^b;
            if(need == a) {
                w.p((a+2));
            } else w.p(a+1);
        }
    }

}