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
from sys import stdin, stdout
from bisect import bisect_right as br

n, q = map(int, raw_input().split())
coins = map(int, raw_input().split())

d = {1 << i : 0 for i in xrange(31)}
for num in coins:
    d[num] += 1

inp = stdin.readlines()
out = []
for line in inp:
    b = int(line.strip())
    ans = 0
    p = 30
    while p >= 0:
        val = 1 << p
        if val <= b:
            sub = min(d[val], b // val)
            ans += sub
            b = b - val * sub
        p -= 1
        
    if b == 0: out.append(str(ans))
    else: out.append(str("-1"))
            
stdout.write('\n'.join(out))
