Iva & Pav
Description
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 $-1$.
Input
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 $2 \cdot 10^5$.
Output
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 $-1$.
3
5
15 14 17 42 34
3
1 7
2 15
4 5
5
7 5 3 1 7
4
1 7
5 7
2 3
2 2
7
19 20 15 12 21 7 11
4
1 15
4 4
7 12
5 7
2 -1 5
1 5 2 2
2 6 -1 5
Note
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 $2$.