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.
//Input
import java.util.Scanner;
import java.io.BufferedReader;
import java.io.InputStreamReader;
//Output
import java.io.PrintWriter;
//DataStructure
import java.util.Arrays;
import java.util.ArrayList;
import java.util.LinkedList;
import java.util.Vector;
import java.util.Map;
import java.util.HashMap;
import java.util.TreeMap;
import java.util.LinkedHashMap;
import java.util.HashSet;
import java.util.TreeSet;
import java.util.LinkedHashSet;
import java.util.Collections;
import java.util.Collection;
//Maths
import static java.lang.Math.abs;
import static java.lang.Math.ceil;
import static java.lang.Math.floor;
import static java.lang.Math.max;
import static java.lang.Math.min;

public class codeB {

    public static void main(String[] args) throws Exception {
        BufferedReader sc = new BufferedReader(new InputStreamReader(System.in));
        long xorArr[] = new long[300000+1];
        xorArr[0] = 0;
        xorArr[1] = 1;
        for(int i = 2; i < xorArr.length; i++){
            xorArr[i] = i^xorArr[i-1];
        }
        
        int testCase = Integer.parseInt(sc.readLine());
        while (testCase-- > 0) {
            String s[] = sc.readLine().split(" ");
            int a = Integer.parseInt(s[0]);
            int b = Integer.parseInt(s[1]);
            if(xorArr[a-1]==b){
                System.out.println(a);
            }
            else if((xorArr[a-1]^b)!=a){
                System.out.println(a+1);
            }
            else{
                System.out.println(a+2);
            }
        }
    }
}