Coins and Queries
Ira has a collection of n coins, each with a denomination represented by a[i]. It is guaranteed that each denomination is a natural power of 2, meaning a[i] = 2^d, where 0 ≤ d.
Ira needs to answer q queries. Each query is defined by an integer b[j]. The task is to determine the minimum number of coins required to achieve the sum b[j] using Ira's coins. If it is not possible to form the sum b[j], the answer for that query should be -1.
Note that answering a query does not alter the collection of coins Ira possesses.
Input
The first line contains two integers n and q (1 ≤ n, q ≤ 2·10^5) – representing the number of coins and the number of queries, respectively.
The second line lists n integers a[1], a[2], ..., a[n] (1 ≤ a[i] ≤ 2·10^9) – these are the denominations of the coins.
The following q lines each contain a single integer b[j] (1 ≤ b[j] ≤ 10^9) – representing each query.
Output
Output q integers ans[j], where the j-th integer is the answer to the j-th query.