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 sys
def get_ints(): return map(int, sys.stdin.readline().strip().split())
def get_list(): return list(map(int, sys.stdin.readline().strip().split()))
def get_string(): return sys.stdin.readline().strip()
def get_int(): return int(sys.stdin.readline().strip())
def get_list_strings(): return list(map(str, sys.stdin.readline().strip().split()))


# Output for list
# sys.stdout.write(" ".join(map(str, final)) + "\n")

# Output for int or str
# sys.stdout.write(str(best) + "\n")



def solve(a, b, array):
  ans = a

  xor = array[a-1]

  if xor == b:
    sys.stdout.write(str(ans) + "\n")
    return
  
  req = xor^b

  if req == a:
    ans += 2
  else:
    ans += 1
  
  sys.stdout.write(str(ans) + "\n")
  return








xorArray = [0]
up = 3*(10**5)

for i in range(1, up+1):
  ele = xorArray[-1]^i

  xorArray.append(ele)



T = get_int()
while T:
  a, b = get_ints()
  solve(a, b, xorArray)
  T -= 1
