description: 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].
solution: #include <bits/stdc++.h>
  using namespace std;
  int n, m;
  int a[4010];
  int d[4010], top;
  int ls[4010], rs[4010];
  long long f[4010][4010];
  int siz[4010];
  void dfs(int x) {
    if (!x) return;
    dfs(ls[x]);
    dfs(rs[x]);
    if (siz[ls[x]] > siz[rs[x]]) swap(ls[x], rs[x]);
    siz[x] = siz[ls[x]] + siz[rs[x]] + 1;
    for (int i = 0; i <= siz[x]; i++) {
      for (int j = 0; j <= siz[ls[x]] && j <= i; j++) {
        if (i - j <= siz[rs[x]])
          f[x][i] = max(f[x][i],
                        f[ls[x]][j] + f[rs[x]][i - j] - 2ll * j * (i - j) * a[x]);
        if (j < i && i - j - 1 <= siz[rs[x]])
          f[x][i] =
              max(f[x][i], f[ls[x]][j] + f[rs[x]][i - j - 1] + 1ll * m * a[x] -
                               (2ll * j * (i - j - 1) + 2ll * i - 1) * a[x]);
      }
    }
  }
  int main() {
    cin >> n >> m;
    for (int i = 1; i <= n; i++) scanf("%d", &a[i]);
    for (int i = 1; i <= n; i++) {
      while (top && a[d[top]] > a[i]) ls[i] = d[top--];
      if (top) rs[d[top]] = i;
      d[++top] = i;
    }
    dfs(d[1]);
    cout << f[d[1]][m];
  }
  