CF1878E.Iva & Pav

Iva and Pav are a famous Serbian competitive programming couple. In Serbia, they call Pav "papuca" and that's why he will make all of Iva's wishes come true.

Iva gave Pav an array $a$ of $n$ elements.

Let's define $f(l, r) = a_l \ \& \ a_{l+1} \ \& \dots \& \ a_r$ (here $\&$ denotes the bitwise AND operation).

Note that $f(l, r)$ is not defined when $l>r$ .

Iva also gave Pav $q$ queries.

Each query consists of 2 numbers, $k$ and $l$ , and she wants Pav to find the largest index $r$ ( $l \le r \le n$ ), such that $f(l, r) \ge k$ .

Pav wants to solve this problem fast because he doesn't want to upset Iva. He needs your help.

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 a single integer $n$ ( $1 \le n \le 2 \cdot 10^5$ ) — the length of array $a$ .

The second line of each test case contains $n$ integers $a_1, a_2, \dots, a_n$ ( $1 \le a_i \le 10^9$ ) — the elements of array $a$ .

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

The next $q$ lines of each test case contains two numbers, $l$ and $k$ ( $1 \le l \le n$ , $1 \le k \le 10^9$ ) — the left bound for the subsegment, and the integer $k$ described in statement.

It is guaranteed that the sum of $n$ over all test cases does not exceed $2 \cdot 10^5$ . Also, it is guaranteed that the sum of $q$ over all test cases does not exceed $2 \cdot 10^5$ .

For each query output maximal index $r$ ( $l \le r \le n$ ) such that $a_l \ \& \ a_{l+1} \ \& \dots \& \ a_r \ \ge \ k$ .

If such $r$ doesn't exist, output $-1$ .

In the first test case $n=5$ , and the array $a = [15, 14, 17, 42, 34]$

The first query asks for the biggest index $r$ such that the $f(1, r) \ge 7$ .

$f(1,1) = 15, \ f(1, 2) = 14, \ f(1,3)=0 \ f(1, 4)=0 \ f(1, 5)=0$ , so $r=2$ is the answer.

The second query asks for $f(2, r) \ge 15$ . Since such $r$ doesn't exist, the answer is $-1$ .

The third query asks for $f(4, r) \ge 5$ . $f(4, 4) = 42, \ f(4, 5) = 34$ , so $r=5$ is the answer.

In the second test case $n=5$ , and the array $a= [7, 5, 3, 1, 7]$ .

For the first query, $f(1, r) \ge 7$ .

$f(1, 1)=7, \ f(1, 2)=5, \ f(1, 3) = 1, \ f(1,4) = 1, \ f(1, 5)=1$ , so the answer to this query is $1$ .

For the second query, $f(5, r) \ge 7$ .

$f(5, 5) = 7$ , so the answer is $5$ .

For the third query, $f(2, r) \ge 3$ .

$f(2, 2) = 5, \ f(2, 3) = 1, \ f(2, 4) = 1, \ f(2, 5) = 1$ , so the answer is $2$ .