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;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.util.StringTokenizer;

public class MexOr {
	static PrintWriter pw = new PrintWriter(new OutputStreamWriter(System.out));
	
	public static void main(String[] args) {
		int[] xor_prefix = new int[1_000_000];
		for(int i = 1; i < xor_prefix.length; i++)
		{
			xor_prefix[i] = xor_prefix[i-1]^i;
		}
		int t = nextInt();
		while (t-- != 0) {
			int a = nextInt(), b = nextInt();
			int needed = xor_prefix[a-1] ^ b;
			if(needed == 0)
				pw.println(a);
			else if(needed == a)
				pw.println(a+2);
			else {
				pw.println(a+1);
			}
			
		}
		pw.flush();
		pw.close();
	}
	static StringTokenizer st;
	static BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
 
	public static String nextLine() {
		String s = "";
		try {
			s = br.readLine();
		} catch (IOException e) {
			// TODO Auto-generated catch block
			e.printStackTrace();
		}
		return s;
	}
 
	public static String next() {
		while (st == null || !st.hasMoreElements()) {
			try {
				st = new StringTokenizer(br.readLine());
			} catch (IOException e) {
				e.printStackTrace();
			}
		}
		return st.nextToken();
	}
 
	public static int nextInt() {
		return Integer.parseInt(next());
	}
	public static long nextLong() {
		return Long.parseLong(next());
	}
}
