Polycarp has n coins, the value of the i-th coin is a_i. It is guaranteed that all the values are integer powers of 2 (i.e. a_i = 2^d for some non-negative integer number d).

Polycarp wants to know answers on q queries. The j-th query is described as integer number b_j. The answer to the query is the minimum number of coins that is necessary to obtain the value b_j using some subset of coins (Polycarp can use only coins he has). If Polycarp can't obtain the value b_j, the answer to the j-th query is -1.

The queries are independent (the answer on the query doesn't affect Polycarp's coins).

Input

The first line of the input contains two integers n and q (1 ≤ n, q ≤ 2 ⋅ 10^5) — the number of coins and the number of queries.

The second line of the input contains n integers a_1, a_2, ..., a_n — values of coins (1 ≤ a_i ≤ 2 ⋅ 10^9). It is guaranteed that all a_i are integer powers of 2 (i.e. a_i = 2^d for some non-negative integer number d).

The next q lines contain one integer each. The j-th line contains one integer b_j — the value of the j-th query (1 ≤ b_j ≤ 10^9).

Output

Print q integers ans_j. The j-th integer must be equal to the answer on the j-th query. If Polycarp can't obtain the value b_j the answer to the j-th query is -1.

Example

Input

5 4
2 4 8 2 4
8
5
14
10


Output

1
-1
3
2
import java.io.*;
import java.util.*;

public class Main{
    
    public static void main(String[] args) throws IOException {
        int n=in.nextInt();
        int q=in.nextInt();
        TreeMap<Integer, Integer> map = new TreeMap(Collections.reverseOrder());
        
        for(int i=0;i<n;i++){
            int a = in.nextInt();
            map.put(a, map.getOrDefault(a, 0)+1);
        }
        
        for(int query=0;query<q;query++){
            int b=in.nextInt();
            int res=0;
            for(int k: map.keySet()){
                int num = k;
                int cnt = map.get(k);
                int multiplier = Math.min(cnt, b/num);
                b = b - multiplier*num;
                res+=multiplier;
            }
            
            if(b==0){
                println(res);
            }
            else{
                println(-1);
            }
        }
        in.close();
        out.close();
    }

    static int MIN = Integer.MIN_VALUE;
    static int MAX = Integer.MAX_VALUE;
    static Reader in = new Reader();
    static PrintWriter out = new PrintWriter(System.out);
    static void read(int arr[], int N) throws IOException{ for(int i=0;i<N;i++){ arr[i]=in.nextInt(); } }
    static void read(long arr[], int N) throws IOException{ for(int i=0;i<N;i++){ arr[i]=in.nextLong(); } }
    static void read(String arr[], int N) throws IOException{ for(int i=0;i<N;i++){ arr[i]=in.next(); } }
    static void print(Object O){ out.print(O); }
    static void println(Object O){ out.println(O); }
    static void print(int arr[]){ for(int i=0;i<arr.length;i++){ print(arr[i]+" "); } println(""); }
    static void print(int arr[][]){ for(int i=0;i<arr.length;i++){ print(arr[i]); } }
    static void debug(Object O){ System.out.println(O); }
}

class Reader {
    BufferedReader reader;
    StringTokenizer tokenizer;

    Reader() {
        reader = new BufferedReader(new InputStreamReader(System.in));
        tokenizer = new StringTokenizer("");
    }

    String next() throws IOException {
        while (!tokenizer.hasMoreTokens() ) { tokenizer=new StringTokenizer(reader.readLine()); }
        return tokenizer.nextToken();
    }

    int nextInt() throws IOException { return Integer.parseInt(next()); }
    double nextDouble() throws IOException { return Double.parseDouble(next()); }
    long nextLong() throws IOException { return Long.parseLong(next()); }
    String nextLine() throws IOException { return reader.readLine(); }
    void close() throws IOException { reader.close(); }
}