The Boss's Identity

给定一个无穷长的整数数列的前 $n$ 项 $a_1,a_2 \dots a_n$，且对于任意 $i > n$，$a_i=a_{i-n}|a_{i-n+1}$. 你需要处理 $q$ 次询问。每次询问给定一个整数 $x$，请找出最小的 $i$ 满足 $a_i>x$。如果不存在这样的 $i$，输出 ```−1``` 。

While tracking Diavolo's origins, Giorno receives a secret code from Polnareff. The code can be represented as an infinite sequence of positive integers: $ a_1, a_2, \dots $ . Giorno immediately sees the pattern behind the code. The first $ n $ numbers $ a_1, a_2, \dots, a_n $ are given. For $ i > n $ the value of $ a_i $ is $ (a_{i-n}\ |\ a_{i-n+1}) $ , where $ | $ denotes the [bitwise OR operator](https://en.wikipedia.org/wiki/Bitwise_operation#OR). Pieces of information about Diavolo are hidden in $ q $ questions. Each question has a positive integer $ v $ associated with it and its answer is the smallest index $ i $ such that $ a_i > v $ . If no such $ i $ exists, the answer is $ -1 $ . Help Giorno in answering the questions!

Each test contains multiple test cases. The first line contains the number of test cases $ t $ ( $ 1 \le t \le 10\,000 $ ). The description of the test cases follows. The first line of each test case contains two integers $ n $ and $ q $ ( $ 2 \leq n \leq 2 \cdot 10^5 $ , $ 1 \leq q \leq 2 \cdot 10^5 $ ). The second line of each test case contains $ n $ integers $ a_1,a_2,\ldots,a_n $ ( $ 0 \leq a_i \leq 10^9 $ ) — the parts of the code which define the pattern. The $ i $ -th line of the next $ q $ lines contain a single integer $ v_i $ ( $ 0 \leq v_i \leq 10^9 $ ) — the question Giorno asks you. The sum of $ n $ and $ q $ over all test cases does not exceed $ 2 \cdot 10^5 $ .

Print $ q $ numbers. The $ i $ -th number is the answer to the $ i $ -th question asked by Giorno.

3
2 3
2 1
1
2
3
4 5
0 2 1 3
0
1
2
3
4
5 5
1 2 3 4 5
7
2
6
0
4

1
3
-1
2
2
4
-1
-1
-1
3
8
1
5

In the first test case, $ a = [2,1,3,3,\ldots] $ . - For the first question, $ a_1=2 $ is the element with the smallest index greater than $ 1 $ . - For the second question, $ a_3=3 $ is the element with the smallest index greater than $ 2 $ . - For the third question, there is no index $ i $ such that $ a_i > 3 $ .