A. Valeriy and Dequetime limit per test6 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputRecently, on the course of algorithms and data structures, Valeriy learned how to use a deque. He built a deque filled with n elements. The i-th element is a_i (i = 1, 2, \ldots, n). He gradually takes the first two leftmost elements from the deque (let's call them A and B, respectively), and then does the following: if A > B, he writes A to the beginning and writes B to the end of the deque, otherwise, he writes to the beginning B, and A writes to the end of the deque. We call this sequence of actions an operation.For example, if deque was [2, 3, 4, 5, 1], on the operation he will write B=3 to the beginning and A=2 to the end, so he will get [3, 4, 5, 1, 2].The teacher of the course, seeing Valeriy, who was passionate about his work, approached him and gave him q queries. Each query consists of the singular number m_j (j = 1, 2, \ldots, q). It is required for each query to answer which two elements he will pull out on the m_j-th operation.Note that the queries are independent and for each query the numbers A and B should be printed in the order in which they will be pulled out of the deque.Deque is a data structure representing a list of elements where insertion of new elements or deletion of existing elements can be made from both sides.InputThe first line contains two integers n and q (2 \leq n \leq 10^5, 0 \leq q \leq 3 \cdot 10^5) — the number of elements in the deque and the number of queries. The second line contains n integers a_1, a_2, ..., a_n, where a_i (0 \leq a_i \leq 10^9) — the deque element in i-th position. The next q lines contain one number each, meaning m_j (1 \leq m_j \leq 10^{18}).OutputFor each teacher's query, output two numbers A and B — the numbers that Valeriy pulls out of the deque for the m_j-th operation.ExamplesInput
5 3
1 2 3 4 5
1
2
10
Output
1 2
2 3
5 2
Input
2 0
0 0
Output
Note Consider all 10 steps for the first test in detail: [1, 2, 3, 4, 5] — on the first operation, A and B are 1 and 2, respectively.So, 2 we write to the beginning of the deque, and 1 — to the end.We get the following status of the deque: [2, 3, 4, 5, 1]. [2, 3, 4, 5, 1] \Rightarrow A = 2, B = 3. [3, 4, 5, 1, 2] [4, 5, 1, 2, 3] [5, 1, 2, 3, 4] [5, 2, 3, 4, 1] [5, 3, 4, 1, 2] [5, 4, 1, 2, 3] [5, 1, 2, 3, 4] [5, 2, 3, 4, 1] \Rightarrow A = 5, B = 2. 
5 3
1 2 3 4 5
1
2
10

1 2 2 3 5 2 
['data structures', 'implementation', '*1500']