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 = 4005;
  int n, m, a[N], sz[N];
  long long f[N][N], g[N];
  void merge_(int u, int v) {
    for (int i = 0; i <= sz[u] + sz[v]; i++) g[i] = 0;
    for (int i = 0; i <= sz[u]; i++)
      for (int j = 0; j <= sz[v]; j++)
        g[i + j] = max(g[i + j], f[u][i] + f[v][j] - 2ll * i * j * a[u]);
    sz[u] += sz[v];
    for (int i = 0; i <= sz[u]; i++) f[u][i] = g[i];
  }
  int solve_(int l, int r) {
    if (l > r) return 0;
    int p = 0;
    for (int i = l; i <= r; i++)
      if (!p || a[p] > a[i]) p = i;
    int lc = solve_(l, p - 1), rc = solve_(p + 1, r);
    f[p][1] = (m - 1ll) * a[p], sz[p] = 1;
    merge_(p, lc);
    merge_(p, rc);
    return p;
  }
  int main() {
    scanf("%d%d", &n, &m);
    for (int i = 1; i <= n; i++) scanf("%d", &a[i]);
    int rt = solve_(1, n);
    printf("%lld\n", f[rt][m]);
  }
  