### ** Frog 3**

### Problem Statement

There are `N` stones, numbered `1, 2, …, N`.
For each `i` (`1 ≤ i ≤ N`), the height of Stone `i` is `h`_{i}.
Here, `h`_{1} < h_{2} < … < h_{N} holds.

There is a frog who is initially on Stone `1`.
He will repeat the following action some number of times to reach Stone `N`:

- If the frog is currently on Stone
`i`, jump to one of the following: Stone `i + 1, i + 2, …, N`. Here, a cost of `(h`_{j} - h_{i})^{2} + C is incurred, where `j` is the stone to land on.

Find the minimum possible total cost incurred before the frog reaches Stone `N`.

### Constraints

- All values in input are integers.
`2 ≤ N ≤ 2 × 10`^{5}
`1 ≤ C ≤ 10`^{12}
`1 ≤ h`_{1} < h_{2} < … < h_{N} ≤ 10^{6}

### Input

Input is given from Standard Input in the following format:

`N` `C`
`h`_{1} `h`_{2} `\ldots` `h`_{N}

### Output

Print the minimum possible total cost incurred.

### Sample Input 1

5 6
1 2 3 4 5

### Sample Output 1

20

If we follow the path `1` → `3` → `5`, the total cost incurred would be `((3 - 1)`^{2} + 6) + ((5 - 3)^{2} + 6) = 20.

### Sample Input 2

2 1000000000000
500000 1000000

### Sample Output 2

1250000000000

The answer may not fit into a 32-bit integer type.

### Sample Input 3

8 5
1 3 4 5 10 11 12 13

### Sample Output 3

62

If we follow the path `1` → `2` → `4` → `5` → `8`, the total cost incurred would be `((3 - 1)`^{2} + 5) + ((5 - 3)^{2} + 5) + ((10 - 5)^{2} + 5) + ((13 - 10)^{2} + 5) = 62.