Z-Frog 3

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.

Input

First line contains two integers n (2 ≤ n ≤ 2 * 10^5) and c (1 ≤ c ≤ 10^12). Second line contains the heights of stones 1 ≤ h[1] < h[2] < ... < h[n] ≤ 10^6.

Output

Print the minimum possible total cost incurred.

Examples