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 sun.reflect.generics.tree.Tree;

import java.io.*;
import java.util.*;
public class Main {
    public static void main(String args[])
    {
        FastReader input=new FastReader();
        PrintWriter out=new PrintWriter(System.out);
        int T=1;
        while(T-->0)
        {
            int n=input.nextInt();
            int q=input.nextInt();
            TreeMap<Integer,Integer> map=new TreeMap<>(Comparator.reverseOrder());
            for(int i=0;i<n;i++)
            {
                int a=input.nextInt();
                if(map.containsKey(a))
                {
                    map.put(a,map.get(a)+1);
                }
                else
                {
                    map.put(a,1);
                }
            }
            ArrayList<Pair> list=new ArrayList<>();
            while(!map.isEmpty())
            {
                int v=map.firstKey();
                int r=map.get(v);
                list.add(new Pair(v,r));
                map.remove(v);
            }
            for(int i=0;i<q;i++)
            {
                int v=input.nextInt();
                int ans=0;
                for(int j=0;j<list.size() && v>0;j++)
                {
                    if(v>=list.get(j).v)
                    {
                        int t=v/list.get(j).v;
                        t=Math.min(t,list.get(j).r);
                        ans+=t;
                        v-=t*list.get(j).v;
                    }
                }
                if(v>0)
                {
                    out.println(-1);
                }
                else
                {
                    out.println(ans);
                }
            }
        }
        out.close();
    }
    public static class Pair
    {
        int v,r;
        Pair(int v,int r)
        {
            this.v=v;
            this.r=r;
        }
    }
    static class FastReader
    {
        BufferedReader br;
        StringTokenizer st;
        public FastReader()
        {
            br = new BufferedReader(new InputStreamReader(System.in));
        }
        String next()
        {
            while (st == null || !st.hasMoreElements())
            {
                try
                {
                    st = new StringTokenizer(br.readLine());
                }
                catch (IOException e)
                {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }
        int nextInt()
        {
            return Integer.parseInt(next());
        }
        long nextLong()
        {
            return Long.parseLong(next());
        }
        double nextDouble()
        {
            return Double.parseDouble(next());
        }
        String nextLine()
        {
            String str="";
            try
            {
                str=br.readLine();
            }
            catch (IOException e)
            {
                e.printStackTrace();
            }
            return str;
        }
    }
}