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 C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <iostream>
#include <vector>
#include <set>
#include <functional>
template <typename T>
struct Line
{
    T a, b;  // (a,b) <=> f(x)=ax+b
    bool query;
    mutable std::function<const Line*()> succ = nullptr;
    bool operator<(const Line& l) const
    {
        if (not l.query) { return a > l.a; }
        const Line* s = succ();
        if (not s) { return false; }
        return s->b - b < (a - s->a) * l.a;
    }
};
template <typename T>
class DynamicCHT : public std::multiset<Line<T>>
{
    bool needless(const typename DynamicCHT<T>::iterator y) const
    {
        const auto z = std::next(y);
        if (y == this->begin()) { return z != this->end() and y->a == z->a and y->b >= z->b; }
        const auto x = std::prev(y);
        return z == this->end() ? y->a == x->a and y->b >= x->b : (x->b - y->b) * (z->a - y->a) >= (y->b - z->b) * (y->a - x->a);
    }

public:
    void add(const T a, const T b)
    {
        auto y = this->insert({a, b, false});
        y->succ = [=]() { return std::next(y) == this->end() ? nullptr : &*std::next(y); };
        if (needless(y)) { return (void)this->erase(y); }
        while (std::next(y) != this->end() and needless(std::next(y))) { this->erase(std::next(y)); }
        while (y != this->begin() and needless(std::prev(y))) { this->erase(std::prev(y)); }
    }
    T query(const T x) const
    {
        const auto l = *this->lower_bound(Line<T>{x, 0, true});
        return l.a * x + l.b;
    }
};
using ll = long long;
int main()
{
    std::size_t N;
    ll C;
    std::cin >> N >> C;
    std::vector<ll> h(N), dp(N);
    for (std::size_t i = 0; i < N; i++) { std::cin >> h[i]; }
    DynamicCHT<ll> cht;
    cht.add(-2 * h[0], dp[0] + h[0] * h[0]);
    for (std::size_t i = 0; i < N; i++) {
        dp[i] = cht.query(h[i]) + h[i] * h[i] + C;
        cht.add(-2 * h[i], dp[i] + h[i] * h[i]);
    }
    std::cout << dp[N - 1] << std::endl;
    return 0;
}