Score : $100$ points

Problem Statement

There are $N$ stones, numbered $1, 2, \ldots, N$. For each $i$ ($1 \leq i \leq N$), the height of Stone $i$ is $h_i$. Here, $h_1 < h_2 < \cdots < h_N$ 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 $i + 1, i + 2, \ldots, N$. 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.
• $2 \leq N \leq 2 \times 10^5$
• $1 \leq C \leq 10^{12}$
• $1 \leq h_1 < h_2 < \cdots < h_N \leq 10^6$

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.

5 6
1 2 3 4 5

20

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

2 1000000000000
500000 1000000

1250000000000

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

8 5
1 3 4 5 10 11 12 13

62

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