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.
// package codeforces;

import java.io.BufferedReader;
import java.io.BufferedWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.util.StringTokenizer;

public class Contest742_Div2 {
	static int nextInt() throws IOException {
		return Integer.parseInt(next());
	}

	static long nextLong() throws IOException {
		return Long.parseLong(next());
	}

	private static String next() throws IOException {

		while (st == null || !st.hasMoreTokens()) {
			st = new StringTokenizer(br.readLine());
		}
		return st.nextToken();
	}

	static BufferedReader br;
	static StringTokenizer st;
	static BufferedWriter bw ;
	static int len=(int)300001;
	static int[]x;
	public static void main(String[] args) throws IOException {
		br = new BufferedReader(new InputStreamReader(System.in));
		bw = new BufferedWriter(new OutputStreamWriter(System.out));
		int t=nextInt();
		x=new int[len];
		for(int i=1;i<len;i++) {
			x[i]=x[i-1]^i;
		}
		while(t-->0) {
			MEXor_Mixup();
		}
		bw.close();
	}
	
	public static void MEXor_Mixup() throws IOException{
		int a=nextInt();
		int b=nextInt();
		if(a==1 && b==1){
			bw.append(3+"\n");
			return;
		}
		if(x[a-1]==b) {
			bw.append(a+"\n");
		}else {
			bw.append(a+1+"\n");
		}
		
	}

	private static void Domino_disaster() throws IOException{
		int n=nextInt();
		char[] s=next().toCharArray();
		for(int i=0;i<n;i++) {
			if(s[i]=='U') {
				s[i]='D';
			}else if(s[i]=='D') {
				s[i]='U';
			}
		}
		String str=String.valueOf(s);
		bw.append(str+"\n");
	}
	
	
	
}
