A construction company has recently imported $n$ wooden poles with varying heights, denoted as $A_1, A_2, \ldots, A_n$. The company has $m$ house designs, with the $i$-th design requiring $S_i$ poles.
The cost of building a house is determined by the difference between the maximum and minimum pole heights, multiplied by a predefined constant $C$. Let $max$ and $min$ represent the maximum and minimum heights of the poles used, respectively. Upon completing a house, the company receives a payment of $P$. Hence, the profit from constructing a house is given by $P - (max - min)^2 \times C$. It is important to note that this value can be negative.
The objective is to find the maximum profit while ensuring that at least one house from each design is built.
### Input
- The first line contains four integers $n,m,P,C$.
- The second line contains $n$ integers $A_i$.
- The third line contains $m$ integers $S_i$.
- It is guaranteed that $\sum_{i=1}^{m} S_i \le n$ and $S_i \neq S_j$ for $1 \le i < j \le m$.
### Output
- Print an integer, the maximum profit.
### Constraints
- $1 \le n \le 10^5$.
- $1 \le m \le 6$.
- $1 \le P \le 10^9$.
- $1 \le C \le 10^6$.
- $1 \le A_i \le 10^6$.
- $2 \le S_i \le n$.
### Example
Input:
```
10 2 11 1
14 5 6 4 4 4 7 8 9 1
4 2
```
Output:
```
30
```
