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 ls[4010], rs[4010];
  int lw[4010], rw[4010];
  int n, a[4010], st[4010], cnt, m;
  long long f[4010][4010];
  int sz[4010];
  void dfs(int x) {
    sz[x]++;
    if (ls[x]) dfs(ls[x]), sz[x] += sz[ls[x]];
    if (rs[x]) dfs(rs[x]), sz[x] += sz[rs[x]];
    for (int i = 0; i <= sz[ls[x]]; i++)
      for (int j = 0; j <= sz[rs[x]]; j++) {
        if (i + j > m)
          break;
        else {
          f[x][i + j] =
              max(f[ls[x]][i] + f[rs[x]][j] + 1ll * i * (m - i) * lw[x] +
                      1ll * j * (m - j) * rw[x],
                  f[x][i + j]);
          f[x][i + j + 1] =
              max(f[ls[x]][i] + f[rs[x]][j] + 1ll * i * (m - i) * lw[x] +
                      1ll * j * (m - j) * rw[x],
                  f[x][i + j + 1]);
        }
      }
  }
  int main() {
    scanf("%d%d", &n, &m);
    for (int i = 1; i <= n; i++) scanf("%d", &a[i]);
    for (int i = 1; i <= n; i++) {
      int pre = cnt;
      while (cnt && a[i] < a[st[cnt]]) cnt--;
      if (cnt) {
        rs[st[cnt]] = i;
        rw[st[cnt]] = a[i] - a[st[cnt]];
      }
      if (cnt < pre) {
        ls[i] = st[cnt + 1];
        lw[i] = a[st[cnt + 1]] - a[i];
      }
      st[++cnt] = i;
    }
    dfs(st[1]);
    printf("%lld\n", f[st[1]][m]);
  }
  