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;
  int n, m, rt, sz[4005];
  int st[4005], top, ch[4005][2];
  long long dp[4005][4005], a[4005];
  void dfs(int now) {
    sz[now] = 1;
    for (int i = 0; i < 2; i++)
      if (ch[now][i]) {
        int to = ch[now][i];
        dfs(to);
        for (int j = sz[now]; j >= 0; j--)
          for (int k = sz[to]; k >= 0; k--)
            dp[now][j + k] =
                max(dp[now][j + k],
                    dp[now][j] + dp[to][k] + k * (m - k) * (a[to] - a[now]));
        sz[now] += sz[to];
      }
  }
  int main() {
    scanf("%d%d", &n, &m);
    for (int i = 1; i <= n; i++) {
      scanf("%lld", &a[i]);
      while (top && a[st[top]] > a[i]) ch[i][0] = st[top--];
      if (top) ch[st[top]][1] = i;
      st[++top] = i;
    }
    for (int i = 1; i <= n; i++)
      if (!rt || a[i] < a[rt]) rt = i;
    dfs(rt);
    printf("%lld", dp[rt][m]);
  }
  