#include <bits/stdc++.h>
template <typename T>
void checkmax(T &x, T y) {
  if (x < y) x = y;
}
template <typename T>
void checkmin(T &x, T y) {
  if (x > y) x = y;
}
int n, m, sz[4001];
long long a[4001], dp[4001][4001];
int Solve(int l, int r) {
  if (l > r) return 0;
  int p = std::min_element(a + l, a + r + 1) - a, u = Solve(l, p - 1),
      v = Solve(p + 1, r);
  sz[p] = sz[u] + sz[v] + 1;
  for (int i = 0; i <= sz[u]; i++)
    for (int j = 0; j <= sz[v]; j++) {
      checkmax(dp[p][i + j], dp[u][i] + dp[v][j] - 2 * a[p] * i * j);
      checkmax(dp[p][i + j + 1], dp[u][i] + dp[v][j] + a[p] * (m - 1) -
                                     2 * a[p] * (i * j + i + j));
    }
  return p;
}
int main(int argc, char const *argv[]) {
  std::ios_base::sync_with_stdio(false);
  std::cin.tie(nullptr), std::cout.tie(nullptr);
  std::cin >> n >> m;
  for (int i = 1; i <= n; i++) std::cin >> a[i];
  std::memset(dp, 0xcf, sizeof(dp));
  dp[0][0] = 0LL;
  std::cout << dp[Solve(1, n)][m];
  return 0;
}

### Prompt

Please create a solution in CPP to the following problem:

Alice has an integer sequence a of length n and all elements are different. She will choose a subsequence of a of length m, and defines the value of a subsequence a_{b_1},a_{b_2},…,a_{b_m} as $$$∑_{i = 1}^m (m ⋅ a_{b_i}) - ∑_{i = 1}^m ∑_{j = 1}^m f(min(b_i, b_j), max(b_i, b_j)), where f(i, j) denotes \min(a_i, a_{i + 1}, \ldots, a_j)$$$.

Alice wants you to help her to maximize the value of the subsequence she choose.

A sequence s is a subsequence of a sequence t if s can be obtained from t by deletion of several (possibly, zero or all) elements.

Input

The first line contains two integers n and m (1 ≤ m ≤ n ≤ 4000).

The second line contains n distinct integers a_1, a_2, …, a_n (1 ≤ a_i < 2^{31}).

Output

Print the maximal value Alice can get.

Examples

Input


6 4
15 2 18 12 13 4


Output


100


Input


11 5
9 3 7 1 8 12 10 20 15 18 5


Output


176


Input


1 1
114514


Output


0


Input


2 1
666 888


Output


0

Note

In the first example, Alice can choose the subsequence [15, 2, 18, 13], which has the value 4 ⋅ (15 + 2 + 18 + 13) - (15 + 2 + 2 + 2) - (2 + 2 + 2 + 2) - (2 + 2 + 18 + 12) - (2 + 2 + 12 + 13) = 100. In the second example, there are a variety of subsequences with value 176, and one of them is [9, 7, 12, 20, 18].

### Response

```cpp
#include <bits/stdc++.h>
template <typename T>
void checkmax(T &x, T y) {
  if (x < y) x = y;
}
template <typename T>
void checkmin(T &x, T y) {
  if (x > y) x = y;
}
int n, m, sz[4001];
long long a[4001], dp[4001][4001];
int Solve(int l, int r) {
  if (l > r) return 0;
  int p = std::min_element(a + l, a + r + 1) - a, u = Solve(l, p - 1),
      v = Solve(p + 1, r);
  sz[p] = sz[u] + sz[v] + 1;
  for (int i = 0; i <= sz[u]; i++)
    for (int j = 0; j <= sz[v]; j++) {
      checkmax(dp[p][i + j], dp[u][i] + dp[v][j] - 2 * a[p] * i * j);
      checkmax(dp[p][i + j + 1], dp[u][i] + dp[v][j] + a[p] * (m - 1) -
                                     2 * a[p] * (i * j + i + j));
    }
  return p;
}
int main(int argc, char const *argv[]) {
  std::ios_base::sync_with_stdio(false);
  std::cin.tie(nullptr), std::cout.tie(nullptr);
  std::cin >> n >> m;
  for (int i = 1; i <= n; i++) std::cin >> a[i];
  std::memset(dp, 0xcf, sizeof(dp));
  dp[0][0] = 0LL;
  std::cout << dp[Solve(1, n)][m];
  return 0;
}

```