Or Permutation codechef solution

Chef has a sequence $A$ of $N$ integers. He picked a non-negative integer $X$ and obtained another sequence $B$ of $N$ integers, defined as $B_{i} = A_{i} ∣ X$ for each $1 \leq i \leq N$ . Unfortunately, he forgot $X$ , and the sequence $B$ got jumbled.

Chef wonders what the value of $X$ is. He gives you the sequence $A$ and the jumbled sequence $B$ . Your task is to find whether there is a non-negative integer $X$ such that there exists a permutation $C$ of $B$ satisfying the condition $C_{i} = A_{i} ∣ X$ for each $1 \leq i \leq N$ .

If there are multiple such $X$ , find any of them.

Note: Here $|$ represents the bitwise OR operation.

Input Format

The first line of the input contains a single integer, $T$ , denoting the number of test cases. The description of $T$ test cases follows.
Each test case consists of 3 lines of input.
- The first line of each test case contains a single integer $N$ .
- The second line of each test case contains $N$ space-separated integers, denoting the sequence $A$ .
- Or Permutation codechef solution
- The third line of each test case contains $N$ space-separated integers, denoting the sequence $B$ .

Output Format

For each test case, output on a new line a single non-negative integer $X$ that satisfies the given condition. If there is no such $X$ , print $- 1$ instead.

Constraints

$1 \leq T \leq 10^{4}$
$1 \leq N \leq 2 \cdot 10^{5}$
$0 \leq A_{i}, B_{i} \leq 10^{9}$ for each $1 \leq i \leq N$
The sum of $N$ over all test cases doesn’t exceed $2 \cdot 10^{5}$

Sample Input 1

Or Permutation codechef solution

3
2
0 1
4 5
3
4 1 2
4 5 2
4
9 13 12 8
11 10 14 15

Sample Output 1

Or Permutation codechef solution

4
-1
2

Explanation

Test case $1$ : Consider $C = [B_{1}, B_{2}] = [4, 5]$ . For $X = 4$ , we have $C_{1} = 4 = 0 ∣ 4$ and $C_{2} = 5 = 1 ∣ 4$ as required.

Test case $2$ : No matter what permutation $C$ of $B$ we choose, there is no such $X$ that satisfies the condition $C_{i} = A_{i} | X$ for all $1 \leq i \leq N$ .

Test case $3$ : Consider $C = [B_{1}, B_{4}, B_{3}, B_{2}] = [11, 15, 14, 10]$ . For $X = 2$ , the condition $C_{i} = A_{i} | X$ is satisfied for all $1 \leq i \leq N$ . Note that $X = 10$ is also a possible answer.

Or Permutation codechef solution

Or Permutation codechef solution

Input Format

Or Permutation codechef solution

Output Format

Constraints

Sample Input 1

Or Permutation codechef solution

Sample Output 1

Or Permutation codechef solution

Explanation

SOLUTION

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