Problem:
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.

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.

Solution in Go (1.6) (judge verdict: Wrong Answer)

package main

import (
	"bufio"
	"fmt"
	"os"
	"strconv"
	"strings"
)

func parseInt(s string) int {
	return int(parseInt64(s))
}

func parseInt64(s string) int64 {
	x, _ := strconv.ParseInt(s, 10, 64)
	return x
}

var reader *bufio.Reader

func readLine() string {
	if reader == nil {
		reader = bufio.NewReader(os.Stdin)
	}
	s, _ := reader.ReadString('\n')
	return strings.TrimSuffix(s, "\n")
}

func readFields() []string {
	return strings.Fields(readLine())
}

type T int64

func max(a, b T) T {
	if a > b {
		return a
	} else {
		return b
	}
}

func min(a, b T) T {
	if a < b {
		return a
	} else {
		return b
	}
}

func sum(a []T) T {
	var result T
	for _, x := range a {
		result += x
	}
	return result
}

func squ(a T) T {
	return a * a
}

var CYCLE T = 1000000007

var LARGE T = 9223372036854775807
var h [200000]T
var c [200000]T

type Line struct {
	a T
	b T
}

var lines [200000]Line
var linesPtr int
var linesLength int

func query(x T) T {
	if linesLength == linesPtr {
		panic("deque is empty")
	}
	result := lines[linesPtr].a*x + lines[linesPtr].b
	for linesPtr < linesLength-1 {
		next := lines[linesPtr+1].a*x + lines[linesPtr+1].b
		if result < next {
			break
		}
		linesPtr++
		result = next
	}
	return result
}

func add(a T, b T) {
	if linesLength > 0 && lines[linesLength-1].a <= a {
		panic("h order is not valid")
	}
	lines[linesLength].a = a
	lines[linesLength].b = b
	linesLength++
}

func main() {
	var N int
	var C T
	fmt.Scan(&N, &C)
	var h0 T
	for i, f := range readFields() {
		h[i] = T(parseInt64(f))
		if i == 0 {
			h0 = h[i]
		}
		h[i] -= h0
	}

	add(0, 0)
	var c T
	for i := 1; i < N; i++ {
		c = query(h[i]) + C + squ(h[i])
		add(-2*h[i], c+squ(h[i]))
	}

	fmt.Printf("%d\n", c)
}