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.*;
import java.lang.*;

public class q4cf {

	public static void main(String[] args) throws IOException {
		BufferedReader x=new BufferedReader(new InputStreamReader(System.in));
		String a=x.readLine();
		String[] b=a.split(" ");
		int n=Integer.parseInt(b[0]);
		int q=Integer.parseInt(b[1]);
		String c=x.readLine();
		String[] d=c.split(" ");
		int[] count=new int[31];
		int[] poww=new int[31];
		for (int w=0;w<31;w++) {
			poww[w]=(int)Math.pow(2,w);
		}
		for (int i=0;i<n;i++) {
			for (int j=0;j<31;j++) {
				
				if (poww[j]==Integer.parseInt(d[i])) {
					count[j]+=1;
					break;
				}
			}
		}
		for (int k=0;k<q;k++) {
			int p=Integer.parseInt(x.readLine());
			int cc=0;
			for (int l=30;l>=0;l--) {
				if (count[l]!=0) {
					int f=poww[l];
					int mm=(int)(p/(f));
					int nn=count[l];
					if (mm<=nn) {
						cc+=mm;
						p=(int)(p%(f));
					}
					else {
						cc+=nn;
						
						p=p-f*count[l];
					}
					if (p==0) {
						break;
					}
						
				}
				
					
			}
			if (p==0) {
				System.out.println(cc);
			}
			else {
				System.out.println(-1);
			}
			
		}
		
		
		

	}

}
