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 = 4005;
  long long f[N][N], a[N];
  int n, m, top, st[N], rt, ls[N], rs[N], s[N];
  int read() {
    int x = 0, f = 1;
    char ch = getchar();
    while (ch < '0' || ch > '9') {
      if (ch == '-') f = -1;
      ch = getchar();
    }
    while (ch >= '0' && ch <= '9') {
      x = x * 10 + ch - '0';
      ch = getchar();
    }
    return x * f;
  }
  void dfs(int x) {
    s[x] = 1;
    if (ls[x] > 0 && rs[x] > 0) {
      dfs(ls[x]), dfs(rs[x]);
      s[x] += s[ls[x]] + s[rs[x]];
      for (int i = 0; i <= min(s[ls[x]], m); i++) {
        for (int j = 0; j <= min(s[rs[x]], m) && i + j <= m; j++) {
          f[x][i + j] =
              max(f[x][i + j], f[ls[x]][i] + f[rs[x]][j] - a[x] * i * j * 2);
          if (i + j < m)
            f[x][i + j + 1] = max(f[x][i + j + 1],
                                  f[ls[x]][i] + f[rs[x]][j] - a[x] * i * j * 2 +
                                      a[x] * (m - 1) - a[x] * (i + j) * 2);
        }
      }
    } else if (ls[x] > 0 || rs[x] > 0) {
      int y = ls[x] ? ls[x] : rs[x];
      dfs(y);
      s[x] += s[y];
      for (int i = 0; i <= min(s[y], m); i++) {
        f[x][i] = max(f[x][i], f[y][i]);
        if (i < m)
          f[x][i + 1] = max(f[x][i + 1], f[y][i] + a[x] * (m - 1) - a[x] * i * 2);
      }
    } else
      f[x][1] = a[x] * (m - 1);
  }
  int main() {
    n = read(), m = read();
    for (int i = 1; i <= n; i++) a[i] = read();
    for (int i = 1; i <= n; i++) {
      int k = top;
      while (k > 0 && a[st[k]] > a[i]) k--;
      if (k > 0) rs[st[k]] = i;
      if (k < top) ls[i] = st[k + 1];
      st[++k] = i;
      top = k;
    }
    rt = 1;
    for (int i = 2; i <= n; i++)
      if (a[rt] > a[i]) rt = i;
    dfs(rt);
    printf("%lld\n", f[rt][m]);
    return 0;
  }
  