#include <bits/stdc++.h>
using namespace std;
mt19937_64 rnd(time(NULL));
const int N = 5010;
long long a[N];
int n, m;
vector<long long> rec(int l, int r) {
  vector<long long> dp(r - l + 2, 0);
  if (l > r) return dp;
  int mn = l;
  for (int i = l + 1; i <= r; i++) {
    if (a[i] < a[mn]) mn = i;
  }
  auto A = rec(l, mn - 1);
  auto B = rec(mn + 1, r);
  vector<long long> cur(2, 0);
  cur[1] = a[mn] * (m - 1ll);
  for (int i = 0; i < A.size(); i++) {
    for (int j = 0; j < B.size(); j++) {
      for (int t = 0; t < cur.size(); t++) {
        dp[i + j + t] =
            max(dp[i + j + t],
                A[i] + B[j] + cur[t] - a[mn] * (i * j + t * i + t * j) * 2ll);
      }
    }
  }
  return dp;
}
void solve() {
  cin >> n >> m;
  for (int i = 1; i <= n; i++) cin >> a[i];
  auto ans = rec(1, n);
  cout << ans[m] << endl;
}
int32_t main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  int tt = 1;
  while (tt--) {
    solve();
  }
  return 0;
}

### Prompt

Your challenge is to write a cpp solution 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>
using namespace std;
mt19937_64 rnd(time(NULL));
const int N = 5010;
long long a[N];
int n, m;
vector<long long> rec(int l, int r) {
  vector<long long> dp(r - l + 2, 0);
  if (l > r) return dp;
  int mn = l;
  for (int i = l + 1; i <= r; i++) {
    if (a[i] < a[mn]) mn = i;
  }
  auto A = rec(l, mn - 1);
  auto B = rec(mn + 1, r);
  vector<long long> cur(2, 0);
  cur[1] = a[mn] * (m - 1ll);
  for (int i = 0; i < A.size(); i++) {
    for (int j = 0; j < B.size(); j++) {
      for (int t = 0; t < cur.size(); t++) {
        dp[i + j + t] =
            max(dp[i + j + t],
                A[i] + B[j] + cur[t] - a[mn] * (i * j + t * i + t * j) * 2ll);
      }
    }
  }
  return dp;
}
void solve() {
  cin >> n >> m;
  for (int i = 1; i <= n; i++) cin >> a[i];
  auto ans = rec(1, n);
  cout << ans[m] << endl;
}
int32_t main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  int tt = 1;
  while (tt--) {
    solve();
  }
  return 0;
}

```