Problem Statement

There is a sequence $a_1, a_2, \dots, a_N$.
Let $\displaystyle S_i = \sum_{j = i}^{i + K - 1} a_j = a_i + a_{i+1} + \dots + a_{i + K - 1}$, and let $S = \{S_1, S_2, \dots, S_{N-K + 1}\}$ be a multiset (added later).
For the $l(1 \le l \le Q)$-th query, output the number of elements of $S$ that are less than or equal to $x_l$.
In other words, output how many of $S_1, S_2, \dots, S_{N - K + 1}$ are less than or equal to $x_l$.

Input

$N\ K$
$a_1\ a_2\ \dots\ a_N$
$Q$
$x_1$
$x_2$
$\dots$
$x_Q$

$1 \le N, Q \le 10^5$
$-10^4 \le a_i \le 10^4$
$1 \le K \le N$
$-10^9 \le x_l \le 10^9$
All inputs are integers.

Output

Output the answers over $Q$ lines, separated by newlines. Print a newline at the end.

Sample

10 2
1 2 3 4 5 6 7 8 9 10
10
19
18
17
15
13
11
9
7
5
3

9
8
8
7
6
5
4
3
2
1