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: Time Limit Exceeded)

package main

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

func max(a, b int) int {
    if a < b {
        return b
    }
    return a
}

func min(a, b int64) int64 {
    if a < b {
        return a
    }
    return b
}

func solve(H []int64, N int64, C int64) int64 {
	dp := make([]int64, N+1)
	for i:=int64(2); i<=N; i++ {
		dp[i] = math.MaxInt64
		for j:=i-1; j>0; j-- {
			dp[i] = min(dp[i], dp[j]+(H[i-1]-H[j-1])*(H[i-1]-H[j-1])+(C))
		}
	}
	return dp[N]
}

func readLineNum(bf *bufio.Reader) int {
	line, _ := bf.ReadString('\n')
	line = strings.Trim(line, "\n")
	N, _ := strconv.Atoi(line)
	return N
}

func readLineNums(bf *bufio.Reader) []int {
	line, _ := bf.ReadString('\n')
	line = strings.Trim(line, "\n")
	fields := strings.Split(line, " ")
	nums := []int{}
	for _, field := range fields {
		num, _ := strconv.Atoi(field)
		nums = append(nums, num)
	}
	return nums
}

func readLine64Nums(bf *bufio.Reader) []int64 {
	line, _ := bf.ReadString('\n')
	line = strings.Trim(line, "\n")
	fields := strings.Split(line, " ")
	nums := []int64{}
	for _, field := range fields {
		num, _ := strconv.ParseInt(field, 10, 64)
		nums = append(nums, num)
	}
	return nums
}

func readLineFloats(bf *bufio.Reader) []float64 {
	line, _ := bf.ReadString('\n')
	line = strings.Trim(line, "\n")
	fields := strings.Split(line, " ")
	fs := []float64{}
	for _, field := range fields {
		f , _ := strconv.ParseFloat(field, 64)
		fs = append(fs, f)
	}
	return fs
}

func readLineStrs(bf *bufio.Reader) []string {
	line, _ := bf.ReadString('\n')
	line = strings.Trim(line, "\n")
	return strings.Split(line, " ")
}

func main() {
	bf := bufio.NewReader(os.Stdin)
    nc := readLine64Nums(bf)
	N, C := nc[0], nc[1]
    H := readLine64Nums(bf)
    fmt.Println(solve(H, N, C))
}