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 = 4e3 + 5;
  int n, m, a[N], top, s[N], lc[N], rc[N], sz[N];
  long long f[N][N];
  void dfs(int x) {
    if (!x) return;
    int l = lc[x], r = rc[x];
    sz[x] = 1, dfs(l), dfs(r), sz[x] += sz[l] + sz[r];
    for (int i = 0; i <= min(sz[l], m); i++)
      for (int j = 0; j <= min(sz[r], m - i); j++) {
        long long w = f[l][i] + f[r][j];
        f[x][i + j] = max(f[x][i + j], w - 1ll * a[x] * i * j * 2);
        f[x][i + j + 1] =
            max(f[x][i + j + 1],
                w + 1ll * a[x] * m - 1ll * a[x] * ((i + 1) * (j + 1) * 2 - 1));
      }
  }
  signed main() {
    scanf("%d%d", &n, &m);
    for (int i = 1; i <= n; i++) {
      scanf("%d", &a[i]);
      while (top && a[s[top]] > a[i]) lc[i] = s[top--];
      if (top) rc[s[top]] = i;
      s[++top] = i;
    }
    dfs(s[1]), printf("%lld\n", f[s[1]][m]);
    return 0;
  }
  