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;
  const int N = 4010;
  int a[N], ls[N], rs[N], sk[N], siz[N], m;
  long long f[N][N];
  void dfs(int x) {
    if (!x) return;
    dfs(ls[x]);
    dfs(rs[x]);
    siz[x] = siz[ls[x]] + siz[rs[x]] + 1;
    for (int i = 0; i <= siz[ls[x]]; i++)
      for (int j = 0; j <= siz[rs[x]]; j++) {
        f[x][i + j] =
            max(f[x][i + j], f[ls[x]][i] + f[rs[x]][j] - 2ll * i * j * a[x]);
        f[x][i + j + 1] =
            max(f[x][i + j + 1], f[ls[x]][i] + f[rs[x]][j] + 1ll * m * a[x] -
                                     (2ll * (i + 1) * (j + 1) - 1) * a[x]);
      }
  }
  signed main() {
    int n, top = 0;
    scanf("%d%d", &n, &m);
    for (int i = 1; i <= n; i++) {
      scanf("%d", a + i);
      int las = 0;
      while (top && a[i] <= a[sk[top]]) las = sk[top--];
      if (las) ls[i] = las;
      if (top) rs[sk[top]] = i;
      sk[++top] = i;
    }
    dfs(sk[1]);
    printf("%lld\n", f[sk[1]][m]);
    return 0;
  }
  