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;
  using ll = long long;
  const ll INF = 1e18;
  const int N = 4000;
  vector<ll> vals[N + 1];
  int pre[N];
  int nxt[N];
  int main() {
    ios_base::sync_with_stdio(false);
    cin.tie(0);
    int n, m;
    cin >> n >> m;
    vector<ll> as(n);
    for (ll& a : as) cin >> a;
    vector<pair<ll, int>> ord(n);
    for (int i = 0; i < n; ++i) {
      ord[i] = {as[i], i};
      pre[i] = i;
    }
    sort(ord.rbegin(), ord.rend());
    for (auto pr : ord) {
      int i = pr.second;
      vector<ll> le, ri;
      int lf = i, rf = i;
      if (i > 0 && as[i - 1] > as[i]) {
        swap(le, vals[pre[i - 1]]);
        lf = pre[i - 1];
      } else {
        le.push_back(0);
      }
      if (i + 1 < n && as[i + 1] > as[i]) {
        swap(ri, vals[i + 1]);
        rf = nxt[i + 1];
      } else {
        ri.push_back(0);
      }
      pre[rf] = lf;
      nxt[lf] = rf;
      vals[lf].resize((int)le.size() + (int)ri.size(), -INF);
      for (int x = 0; x < le.size(); ++x) {
        for (int y = 0; y < ri.size(); ++y) {
          ll off0 = le[x] + ri[y] - 2 * x * y * as[i];
          ll off1 = le[x] + ri[y] + as[i] * (m - 2 * x * y - 2 * x - 2 * y - 1);
          vals[lf][x + y] = max(vals[lf][x + y], off0);
          vals[lf][x + y + 1] = max(vals[lf][x + y + 1], off1);
        }
      }
    }
    cout << vals[0][m] << '\n';
  }
  