An epidemic is seriously affecting people's lives, prompting the city to organize a vaccination campaign across the entire area. Based on addresses, the Centers for Disease Control (CDC) divides the individuals into $n$ groups and mobilizes $m$ nurses to carry out vaccinations at the city's largest hospital. Because the epidemic spreads rapidly, the infection control process in the vaccination area must adhere to a strict procedure as follows:
- Each nurse will participate in vaccinating one group and only one group.
- Nurses working together on a group will work simultaneously, taking exactly 1 minute to vaccinate each person.
- This means that if a group of $p$ people is vaccinated by $q$ nurses, the vaccination time for the entire group will be $⌈\frac{p}{q}⌉$. For example, if a group of 30 people is vaccinated by 4 nurses, the group will complete the vaccination in 8 minutes, but if vaccinated by 5 nurses, it will only take 6 minutes.
Upon completing the vaccination, each group must leave immediately for the next group to begin vaccination.
Requirements: You are given the number of groups $n$, the number of people in each group, and the number of nurses $m$. Find a way to assign each nurse to a group to minimize the total vaccination time for the $n$ groups.
Since during the epidemic, nurses can be suddenly reassigned, you need to plan for $t$ scenarios, each scenario specified by the number of nurses who can participate in the vaccination ($m$).
### Input
- The first line consists of two positive integers $n \le 10^3, t \le 10^4$.
- The second line contains $n$ positive integers $a_1, a_2, ..., a_n$ representing the number of people in each group $(a_i \le 10^4)$.
- The next $t$ lines, each containing a positive integer $m$, represent scenarios with $m$ nurses participating in the vaccination $(n \le m \le 10^4)$.
### Output
- Print $t$ lines, where the $i$-th line is the total vaccination time for the $i$-th scenario, measured in minutes.
### Constraints
- 20% of tests have $n \le 7; t\le10;a_i\le10$.
- 20% of tests have $n \le 60;a_i \le 1000$.
- 20% of tests have $n \le 300;a_i \le 1000$.
- 20% of tests have $n \le 1000;a_i\le1000$.
- The remaining 20% of tests have no additional constraints.
### Example
Input:
```
3 4
6 10 1
3
9
12
4
```
Output:
```
17
5
4
12
```
