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.