CF2199E Supersequence

An array $ a $ is called a subsequence of an array $ b $ if some elements can be removed from array $ b $ (possibly all, possibly none) to obtain the array $ a $ . You are given an array $ a = [a_1, a_2, \dots, a_n] $ . We call an array $ b = [b_1, b_2, \dots, b_m] $ beautiful if: - $ a $ is a subsequence of $ b $ ; - for each $ i $ from $ 1 $ to $ m-1 $ , the elements $ b_i $ and $ b_{i+1} $ differ by exactly $ 1 $ (that is, $ |b_i - b_{i+1}| = 1 $ ); - among all arrays that satisfy these two requirements, the length of $ b $ is minimum. You have to process $ q $ queries. In the $ i $ -th query, a single integer $ x_i $ is given. Your task is as follows: - if $ x_i $ is greater than the minimum possible number of elements in a beautiful array, print $ -1 $ ; - otherwise, if the same number occupies position $ x_i $ in all beautiful arrays, print that number; - otherwise, print $ 0 $ .

The first line contains two integers $ n $ and $ q $ ( $ 1 \le n, q \le 2 \cdot 10^5 $ ). The second line contains $ n $ integers $ a_1, a_2, \dots, a_n $ ( $ 1 \le a_i \le 10^9 $ ). The third line contains $ q $ integers $ x_1, x_2, \dots, x_q $ ( $ 1 \le x_i \le 10^{18} $ ).

For each query, print a single integer — the answer to it.