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>
  const int N = 4005;
  int lc[N], rc[N], st[N], top, val[N], n, m, siz[N];
  long long f[N][N];
  inline int Read() {
    char ch;
    while ((ch = getchar()) < '0' || ch > '9')
      ;
    int x = ch ^ 48;
    while ((ch = getchar()) >= '0' && ch <= '9')
      x = (x << 3) + (x << 1) + (ch ^ 48);
    return x;
  }
  inline void Work(const int i) {
    while (top && val[st[top]] > val[i]) top--;
    int u = st[top];
    lc[i] = rc[u];
    rc[u] = i;
    st[++top] = i;
    return;
  }
  inline long long Max(const long long x, const long long y) {
    return x > y ? x : y;
  }
  inline void Dfs(const int u) {
    if (!u) return;
    Dfs(lc[u]);
    Dfs(rc[u]);
    siz[u] = siz[lc[u]] + siz[rc[u]] + 1;
    for (register int i = 0; i <= siz[lc[u]]; i++) {
      for (register int j = 0; j <= siz[rc[u]]; j++) {
        if (i + j > m) break;
        f[u][i + j] =
            Max(f[u][i + j], f[lc[u]][i] + f[rc[u]][j] - 2ll * i * j * val[u]);
      }
    }
    for (register int i = siz[u]; i; i--)
      f[u][i] = Max(
          f[u][i], f[u][i - 1] + 1ll * (m - 1) * val[u] - 2ll * (i - 1) * val[u]);
    return;
  }
  inline void Init() {
    n = Read();
    m = Read();
    for (register int i = 1; i <= n; i++) {
      val[i] = Read();
      Work(i);
    }
    return;
  }
  int main() {
    Init();
    Dfs(rc[0]);
    printf("%lld\n", f[rc[0]][m]);
    return 0;
  }
  