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.*;
public class ttrryy {
	public static void main(String[] args) {
		@SuppressWarnings("resource")
		Scanner sc=new Scanner(System.in);
	    int t=0;
	    int x[]=new int[300001];
	    for(int i=1;i<300001;i++) {
	    	x[i]=x[i-1]^i;
	    }
	    t=sc.nextInt();
	    int p=0;
	    int ar[]=new int[t];
	    while(t>0) {
	    	t--;
	    	int a=sc.nextInt();
	    	int b=sc.nextInt();
	    	int ans=x[a-1],val=0;
	    	
	    	if(ans!=b) {
	    		int c=0;
	    		c=ans^b;
	    		if(c!=a) {
	    			val=a+1;
	    		}
	    		else {
	    			val=a+2;
	    		}
	    	}
	    	else {
	    		val=a;
	    	}
	    	ar[p++]=val;
	    }
	    System.out.println(Arrays.toString(ar).replace('[',' ').replace(']',' ').replace(',',' ' ));
	}
}