You are given two integers n and m. Find the \operatorname{MEX} of the sequence n ⊕ 0, n ⊕ 1, …, n ⊕ m. Here, ⊕ is the [bitwise XOR operator](https://en.wikipedia.org/wiki/Bitwise_operation#XOR).

\operatorname{MEX} of the sequence of non-negative integers is the smallest non-negative integer that doesn't appear in this sequence. For example, \operatorname{MEX}(0, 1, 2, 4) = 3, and \operatorname{MEX}(1, 2021) = 0. 

Input

The first line contains a single integer t (1 ≤ t ≤ 30 000) — the number of test cases.

The first and only line of each test case contains two integers n and m (0 ≤ n, m ≤ 10^9).

Output

For each test case, print a single integer — the answer to the problem.

Example

Input


5
3 5
4 6
3 2
69 696
123456 654321


Output


4
3
0
640
530866

Note

In the first test case, the sequence is 3 ⊕ 0, 3 ⊕ 1, 3 ⊕ 2, 3 ⊕ 3, 3 ⊕ 4, 3 ⊕ 5, or 3, 2, 1, 0, 7, 6. The smallest non-negative integer which isn't present in the sequence i. e. the \operatorname{MEX} of the sequence is 4.

In the second test case, the sequence is 4 ⊕ 0, 4 ⊕ 1, 4 ⊕ 2, 4 ⊕ 3, 4 ⊕ 4, 4 ⊕ 5, 4 ⊕ 6, or 4, 5, 6, 7, 0, 1, 2. The smallest non-negative integer which isn't present in the sequence i. e. the \operatorname{MEX} of the sequence is 3.

In the third test case, the sequence is 3 ⊕ 0, 3 ⊕ 1, 3 ⊕ 2, or 3, 2, 1. The smallest non-negative integer which isn't present in the sequence i. e. the \operatorname{MEX} of the sequence is 0.
#!/usr/bin/env python3

def msb(x):
	i = 0
	p = 1
	
	assert x != 0

	while (p < x):
		i += 1
		p = p << 1

	return i

def solve():
	n, m = map(int, input().split(" "))
	M = m + 1

	if n == 0:
		if M == 0:
			return 1
		else:
			return 0
	elif m == 0:
		if n + 1 == 0:
			return 1
		else:
			return 0

	ub = max(msb(n), msb(M))
	
	mex = 0
	p = 1 << (ub - 1)
	for bit in range(ub, 0, -1):
		l_bit = (n & p) > 0
		r_bit = (M & p) > 0
		set_this_bit = False

		if r_bit and not l_bit:
			set_this_bit = True
		elif l_bit and not r_bit:
			return mex

		if set_this_bit:
			mex = mex | p
		p = p >> 1

	return mex

def main():
	t = int(input())
	for tt in range(t):
		print(solve())

main()