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>
  int main(void) {
    std::ios::sync_with_stdio(false);
    std::cin.tie(nullptr);
    std::cout.tie(nullptr);
    int N, M;
    std::cin >> N >> M;
    std::vector<int> A(N + 1, 0);
    for (int i = 1; i <= N; ++i) std::cin >> A[i];
    std::vector<int> Sta(N + 1, 0), Ls(N + 1, 0), Rs(N + 1, 0);
    int top = 0, mn = A[1];
    for (int i = 1; i <= N; ++i) {
      while (top && A[Sta[top]] > A[i]) Ls[i] = Sta[top--];
      if (top) Rs[Sta[top]] = i;
      Sta[++top] = i, mn = std::min(mn, A[i]);
    }
    int rt = 0;
    for (int i = 1; i <= N; ++i)
      if (mn == A[i]) rt = i;
    std::vector<std::vector<long long>> dp(N + 1,
                                           std::vector<long long>(M + 1, -1E17));
    std::vector<int> Sz(N + 1, 0);
    auto Merge = [&](int u, int v) {
      if (!v) return;
      std::vector<long long> f(M + 1, -1E18);
      for (int a = 0; a <= Sz[u]; ++a)
        for (int b = 0; b <= Sz[v] && a + b <= M; ++b)
          f[a + b] = std::max(f[a + b], dp[u][a] + dp[v][b] - 2ll * a * b * A[u]);
      dp[u] = f, Sz[u] += Sz[v];
    };
    std::function<void(int)> solve = [&](int u) {
      if (!u) return;
      dp[u][0] = 0, dp[u][1] = 1ll * A[u] * (M - 1), Sz[u] = 1;
      solve(Ls[u]), solve(Rs[u]);
      Merge(u, Ls[u]), Merge(u, Rs[u]);
    };
    solve(rt);
    long long ans = -2E18;
    for (int i = 1; i <= N; ++i) ans = std::max(ans, dp[i][M]);
    std::cout << ans << '\n';
    return 0;
  }
  