The value of a sequence $B$ of $m$ elements is $1 \times B_1 + 2 \times B_2 + ... + m \times B_m$.
Given an array $A$ of $n$ integers, find a subsequences of $k$ elements so that:
- The indices of two consecutive chosen elements differ no more than $m$.
- The value of the subsequence is maximum.
### Input
- The first line contains three integers $n,m,k$.
- The second line contains $n$ integer $A_i$.
### Output
- Print the maximum value of the sequence.
### Constraints
- $1 \le n,m \le 10^5$.
- $1 \le k \le min(n,200)$.
- $1 \le A_i \le 10^9$.
### Example
Input:
```
7 2 3
1 9 2 4 5 3 7
```
Output:
```
35
```