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.util.Comparator;
import java.util.*;

/**
 * @author Yuxuan Wu
 */
public class Main {
    public static final int RANGE = 1000000;
    static int MAX = Integer.MAX_VALUE;
    static int MIN = Integer.MIN_VALUE;
    static int MODULO = 1000000007;
    static Scanner sc = new Scanner(System.in);

    static int multi = 1;

    private static void solve() {
        int mex = sc.nextInt();
        int xor = sc.nextInt();
        int ans = 0;
        if((mex-1) % 4 == 0){
            ans = mex-1;
        }else if((mex-1) % 4 == 1){
            ans = 1;
        }
        else if((mex-1) % 4 == 2){
            ans = mex;
        }
        if(ans == xor){
            System.out.println(mex);
        }
        else{
            int c = ans ^ xor;
            if(c == mex){
                mex++;
            }
            System.out.println(mex+1);
        }
    }
    
    public static void main(String[] args) {
        if(multi == 0){
            solve();
        }
        else {
            int T = sc.nextInt();
            for(int t = 1; t <= T; ++t){
                solve();
            }
        }
    }

    /**
     * 阶乘
     */
    private static int factorial(int n) {
        if(n == 0 || n == 1){
            return n;
        }
        return factorial(n-1) * n;
    }

    /**
     * 返回最大公约数
     * 时间复杂度 O(Log min(n1, n2))
     */
    public static long gcd(long n1, long n2) {
        if (n2 == 0) {
            return n1;
        }
        return gcd(n2, n1 % n2);
    }

    /**
     * 返回该数的位数
     */
    public static int getDigit(long num){
        int ans = 0;
        while(num > 0){
            ans++;
            num /= 10;
        }
        return ans;
    }

    /**
     * 返回该数各位之和
     */
    public static int digitSum(long num) {
        int ans = 0;
        while (num > 0) {
            ans += num % 10;
            num /= 10;
        }
        return ans;
    }

    /**
     * 判断是否为回文串
     */
    public static boolean palindrome(String s) {
        int n = s.length();
        for(int i = 0; i < n; i++) {
            if(s.charAt(i) != s.charAt(n - i - 1)) {
                return false;
            }
        }
        return true;
    }

    /**
     * 判断是否为完全平方数
     */
    public static boolean isSquare(int num) {
        double a = 0;
        try {
            a = Math.sqrt(num);
        } catch (Exception e) {
            return false;
        }
        int b = (int) a;
        return a - b == 0;
    }

    public static class Pairs<K, V> implements Comparable<Pairs> {
        private K key;
        private V value;

        public K getKey() { return key; }
        public V getValue() { return value; }
        public void setKey(K key) {
            this.key = key;
        }
        public void setValue(V value) {
            this.value = value;
        }
        public Pairs( K key,  V value) {
            this.key = key;
            this.value = value;
        }

        @Override
        public String toString() {
            return key + " = " + value;
        }

        @Override
        public boolean equals(Object o) {
            if (this == o) {
                return true;
            }
            if (o == null || getClass() != o.getClass()) {
                return false;
            }
            Pairs<?, ?> pairs = (Pairs<?, ?>) o;
            return Objects.equals(key, pairs.key) &&
                    Objects.equals(value, pairs.value);
        }

        @Override
        public int hashCode() {
            return Objects.hash(key, value);
        }

        @Override
        public int compareTo(Pairs o) {
            return 0;
        }
    }

    static class CompInt implements Comparator<Pairs>{
        @Override
        public int compare(Pairs o1, Pairs o2) {
            if(o1.key instanceof  Integer&&o2.key instanceof  Integer){
                if((int)o1.key>(int)o2.key){
                    return 1;
                }else{
                    return -1;
                }
            }
            return 0;
        }
    }

    static class CompLong implements Comparator<Pairs>{
        @Override
        public int compare(Pairs o1, Pairs o2) {
            return Long.compare((long)o1.key, (long)o2.key);
        }
    }

    static class CompDouble implements Comparator<Pairs>{
        @Override
        public int compare(Pairs o1, Pairs o2) {
            if(o1.key instanceof  Double && o2.key instanceof Double){
                return Double.compare((double) o1.key, (double) o2.key);
            }
            return 0;
        }
    }

    /*
    static class Reader {
        final private int BUFFER_SIZE = 1 << 16;
        private DataInputStream din;
        private byte[] buffer;
        private int bufferPointer, bytesRead;

        public Reader()
        {
            din = new DataInputStream(System.in);
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

        public Reader(String file_name) throws IOException
        {
            din = new DataInputStream(
                    new FileInputStream(file_name));
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

        public String readLine() throws IOException
        {
            byte[] buf = new byte[64]; // line length
            int cnt = 0, c;
            while ((c = read()) != -1) {
                if (c == '\n') {
                    if (cnt != 0) {
                        break;
                    }
                    else {
                        continue;
                    }
                }
                buf[cnt++] = (byte)c;
            }
            return new String(buf, 0, cnt);
        }

        public int nextInt() throws IOException
        {
            int ret = 0;
            byte c = read();
            while (c <= ' ') {
                c = read();
            }
            boolean neg = (c == '-');
            if (neg) {
                c = read();
            }
            do {
                ret = ret * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');

            if (neg) {
                return -ret;
            }
            return ret;
        }

        public long nextLong() throws IOException
        {
            long ret = 0;
            byte c = read();
            while (c <= ' ') {
                c = read();
            }
            boolean neg = (c == '-');
            if (neg) {
                c = read();
            }
            do {
                ret = ret * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');
            if (neg) {
                return -ret;
            }
            return ret;
        }

        public double nextDouble() throws IOException
        {
            double ret = 0, div = 1;
            byte c = read();
            while (c <= ' ') {
                c = read();
            }
            boolean neg = (c == '-');
            if (neg) {
                c = read();
            }

            do {
                ret = ret * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');

            if (c == '.') {
                while ((c = read()) >= '0' && c <= '9') {
                    ret += (c - '0') / (div *= 10);
                }
            }

            if (neg) {
                return -ret;
            }
            return ret;
        }

        private void fillBuffer() throws IOException
        {
            bytesRead = din.read(buffer, bufferPointer = 0,
                    BUFFER_SIZE);
            if (bytesRead == -1) {
                buffer[0] = -1;
            }
        }

        private byte read() throws IOException
        {
            if (bufferPointer == bytesRead) {
                fillBuffer();
            }
            return buffer[bufferPointer++];
        }

        public void close() throws IOException
        {
            if (din == null) {
                return;
            }
            din.close();
        }
    }

     */
}
