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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;

public class B {

    static BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    static final int N = 300005;
    static int[] f = new int[N];

    public static void main(String[] args) throws IOException {
        int t = Integer.parseInt(br.readLine());
        f[0] = 0;
        for(int i = 1; i < N; i++) {
            f[i] = i ^ f[i - 1];
        }
        while(t-- > 0) {
            solve();
        }
    }

    private static void solve() throws IOException {
        final String[] s = br.readLine().split(" ");
        int a = Integer.parseInt(s[0]), b = Integer.parseInt(s[1]);
        if(a == 1) {
            if(b == 1) {
                System.out.println(3);
            } else {
                System.out.println(2);
            }
            return;
        }
        int res = a;
        if(f[a - 1] != b) {
            res++;
            if((f[a - 1] ^ b) == a) res++;
        }
        System.out.println(res);
    }
}
