human
What is a the shortest possible length of the array Bob wrote given the following:
PYTHON3 solution for "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.":
assistant
#Here is the shortest possible length of the array Bob wrote.
 def main():
    test=int(input())
    t=0
    while t<test:
        a,b=map(int,input().split())
        x=0
        count=0
        rem=(a-1)%4
        if rem==0:
            x=a-1
        elif rem==1:
            x=1
        elif rem==2:
            x=a
        else:
            x=0    
        
        if x^a==b:
            count=a+2
        
        elif x==b:
            count=a
        else:
            count=a+1
        print(count)
        t+=1

if __name__=="__main__":
    main()     

""" 5
1 1
2 1
2 0
1 10000
2 10000 """