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Points: 20
Time limit: 1.0s
Memory limit: 256M

Problem type
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These problems are from the atcoder DP contest, and were transferred onto DMOJ. All problem statements were made by several atcoder users. As there is no access to the test data, all data is randomly generated. If there are issues with the statement or data, please contact Ninjaclasher on slack.

There are N stones, numbered 1, 2, \ldots, N. For each i (1 \le i \le N), the height of Stone i is h_i. Here, h_1 < h_2 < \ldots < h_N holds.

There is a frog who is initially at 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 stones: 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 \le N \le 2 \times 10^5
  • 1 \le C \le 10^{12}
  • 1 \le h_1 < h_2 < \ldots < h_N \le 10^6

Input Specification

The first line will contain two integers N, C.

The second line will contain N integers, h_i.

Output Specification

Print the minimum possible total cost incurred.

Sample Input 1

5 6
1 2 3 4 5

Sample Output 1

20

Explanation For Sample 1

If we follow the path 1 \rightarrow 3 \rightarrow 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

Explanation For Sample 2

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

Explanation For Sample 3

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


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