human
PYTHON3 solution for "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.":



Can you provide a Python code to find the \operatorname{MEX} of the sequence n ⊕ 0, n ⊕ 1, …, n ⊕ m?
assistant
#Here is Python code to find the \operatorname{MEX} of the sequence n ⊕ 0, n ⊕ 1, …, n ⊕ m.
 def bit(n):
    res = []
    while n:
        res.append(n%2)
        n//=2
    return res

def tod(s):
    res = 0
    cur = 1
    for i in range(len(s)):
        res += s[i] * cur
        cur *= 2
    return res

for _ in range(int(input())):
    n,m = map(int,input().split())
    q = bit(n)
    w = bit(m)
    res = w[::]
    if m < n:
        print(0)
        continue
    ans = [0 for _ in range(len(q))] + w[len(q):]
    pr = False
    for i in range(len(q)-1,-1,-1):
        if q[i] == 1 and w[i] == 0:
            pr = True
            break
        if q[i] == 0 and w[i] == 1:
            ans[i] = 1
    if not pr:
        for i in range(len(ans)):
            if i < len(q):
                if ans[i] == 0 and q[i] == 0:
                    ans[i] = 1
                    for j in range(i-1,-1,-1):
                        ans[j] = 0
                    break
            else:
                if ans[i] == 0:
                    ans[i] = 1
                    for j in range(i-1,-1,-1):
                        ans[j] = 0
                    break
        else:
            ans = [0 for _ in range(len(ans))] + [1]
    ans = tod(ans)
    print(ans)