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 $$$i \gt n$$$ the value of $$$a_i$$$ is $$$(a_{i-n}\ |\ a_{i-n+1})$$$, where $$$|$$$ denotes the bitwise OR operator.

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 $$$a_i \gt v$$$. If no such $$$i$$$ exists, the answer is $$$-1$$$. Help Giorno in answering the questions!

Input

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 $$$2 \cdot 10^5$$$.

Output

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

Note

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 $$$a_i \gt 3$$$.

The Boss's Identity

Examples