CF1665E.MinimizOR

You are given an array $a$ of $n$ non-negative integers, numbered from $1$ to $n$ .

Let's define the cost of the array $a$ as $\displaystyle \min_{i \neq j} a_i | a_j$ , where $|$ denotes the bitwise OR operation.

There are $q$ queries. For each query you are given two integers $l$ and $r$ ( $l < r$ ). For each query you should find the cost of the subarray $a_{l}, a_{l + 1}, \ldots, a_{r}$ .

Each test case consists of several test cases. The first line contains a single integer $t$ ( $1 \le t \le 10^4$ ) — the number of test cases.

The first line of each test case contains an integer $n$ ( $2 \le n \le 10^5$ ) — the length array $a$ .

The second line of each test case contains $n$ integers $a_1, a_2, \ldots, a_n$ ( $0 \le a_i < 2^{30}$ ) — the elements of $a$ .

The third line of each test case contains an integer $q$ ( $1 \le q \le 10^5$ ) — the number of queries.

Each of the next $q$ lines contains two integers $l_j$ , $r_j$ ( $1 \le l_j < r_j \le n$ ) — the description of the $j$ -th query.

It is guaranteed that the sum of $n$ and the sum of $q$ over all test cases do not exceed $10^5$ .

For each test case print $q$ numbers, where the $j$ -th number is the cost of array $a_{l_j}, a_{l_j + 1}, \ldots, a_{r_j}$ .

In the first test case the array $a$ is

$110_2, 001_2, 011_2, 010_2, 001_2$ .

That's why the answers for the queries are:

• $[1; 2]$ : $a_1 | a_2 = 110_2 | 001_2 = 111_2 = 7$ ;
• $[2; 3]$ : $a_2 | a_3 = 001_2 | 011_2 = 011_2 = 3$ ;
• $[2; 4]$ : $a_2 | a_3 = a_3 | a_4 = a_2 | a_4 = 011_2 = 3$ ;
• $[2; 5]$ : $a_2 | a_5 = 001_2 = 1$ .

In the second test case the array $a$ is

$00_2, 10_2, 01_2, \underbrace{11\ldots 1_2}_{30}$ ( $a_4 = 2^{30} - 1$ ).

That's why the answers for the queries are:

• $[1; 2]$ : $a_1 | a_2 = 10_2 = 2$ ;
• $[2; 3]$ : $a_2 | a_3 = 11_2 = 3$ ;
• $[1; 3]$ : $a_1 | a_3 = 01_2 = 1$ ;
• $[3; 4]$ : $a_3 | a_4 = 01_2 | \underbrace{11\ldots 1_2}_{30} = 2^{30} - 1 = 1073741823$ .