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.util.Scanner;

public class Main {
	
	private static int[] cnt = new int[40];
	
	public static void main(String[] args) {
		
		Scanner scan = new Scanner(System.in);
	
		int i , j , n = scan.nextInt() , q = scan.nextInt();
		for (i = 0;i < n;i ++) {
			int input = scan.nextInt();
			int index = getIndex(input) - 1;
			cnt[index] ++;
		}
		for (i = 0;i < q;i ++) {
			int value = scan.nextInt();
			int ans = 0;
			for (j = 30;j >= 0 && value > 0;j --) {
				int current = (1 << j);
				int need = value / current;
				int temp = Math.min(need , cnt[j]);
				ans += temp;
				value -= temp * current;
			}
			if (value == 0) {
				System.out.println(ans);
			} else {
				System.out.println(- 1);
			}
		}
		
	}
	
	private static int getIndex(int value) {
		
		int ans = 0;
		while (value > 0) {
			value /= 2;
			ans ++;
		}
		return ans;
		
	}
    
}














