There is an array of integers (a_1, a_2, \ldots, a_n), and there is an integer (X). You may perform the following operation zero or more times: Select (i), and increase (a_i) by one. Let (a') be the final state of the array. Your goal is to perform the operation above the smallest number of times such that (a'_1 \,\&\, a'_2 \,\&\, \ldots \,\&\, a'_n = X). (\&) denotes the bitwise AND operation . There are (q) such query integers (X): (X_1, X_2, \ldots, X_q). Compute the answer for each (X = X_i). Note that all queries are processed separately and independently, from the same initial state (a). The first line contains integers (n) and (q) ((2 \le n \le 200\,000), (1 \le q \le 200\,000)) — the length of the array and the number of queries. The second line contains integers (a_1, a_2, \ldots, a_n) (for each (i), (0 \le a_i < 2^{20})). The next (q) lines each contain a single integer (X_i) ((0 \le X_i < 2^{20})). For each query (i) out of (q), print the smallest number of operations to get to the array (a') such that (a'_1 \,\&\, a'_2 \,\&\, \ldots \,\&\, a'_n = X_i). It's possible to show, that it's always possible to obtain such array (a') in finite number of operations. For the first query, you can increase (i = 3) ((a_i = 7)) and get the array (a = 6, 4, 8, 5, 4), then (6 \,\&\, 4 \,\&\, 8 \,\&\, 5 \,\&\, 4 = 0). For the third query, original array already matches condition: (6 \,\&\, 4 \,\&\, 7 \,\&\, 5 \,\&\, 4 = 4).