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;
  using i64 = long long;
  using uint = unsigned int;
  using ui64 = unsigned long long;
  namespace IO {
  template <typename T>
  inline void read(T &x) {
    x = 0;
    bool f = 0;
    char a = getchar();
    for (; !isdigit(a); a = getchar())
      if (a == '-') f = 1;
    for (; isdigit(a); a = getchar()) x = x * 10 + a - '0';
    if (f) x = -x;
  }
  inline int read() {
    int x;
    read(x);
    return x;
  }
  inline i64 readll() {
    i64 x;
    read(x);
    return x;
  }
  }  // namespace IO
  using IO ::read;
  using IO ::readll;
  using vi = vector<int>;
  const int N = 4000 + 5;
  int n, m;
  int a[N], ls[N], rs[N], stk[N], top, fa[N];
  i64 dp[N][N], f[N];
  int sz[N];
  void dfs(int x) {
    sz[x] = 1;
    dp[x][0] = 0;
    dp[x][1] = 1LL * (m - 1) * a[x];
    int y = ls[x];
    if (y) {
      dfs(y);
      memset(f, 0, sizeof(f));
      for (int i = (0); i <= (sz[y]); i++)
        for (int j = (0); j <= (sz[x]); j++) {
          f[i + j] = max(dp[y][i] + dp[x][j] - 2ll * a[x] * i * j, f[i + j]);
        }
      sz[x] += sz[y];
      for (int i = (0); i <= (sz[x]); i++) dp[x][i] = f[i];
    }
    y = rs[x];
    if (y) {
      dfs(y);
      memset(f, 0, sizeof(f));
      for (int i = (0); i <= (sz[y]); i++)
        for (int j = (0); j <= (sz[x]); j++) {
          f[i + j] = max(dp[y][i] + dp[x][j] - 2ll * a[x] * i * j, f[i + j]);
        }
      sz[x] += sz[y];
      for (int i = (0); i <= (sz[x]); i++) dp[x][i] = f[i];
    }
  }
  int main() {
    n = read();
    m = read();
    for (int i = (1); i <= (n); i++) a[i] = read();
    for (int i = (1); i <= (n); i++) {
      int pos = top;
      while (pos && a[stk[pos]] > a[i]) pos--;
      if (pos) rs[stk[pos]] = i;
      if (pos < top) ls[i] = stk[pos + 1];
      stk[top = ++pos] = i;
    }
    for (int i = (1); i <= (n); i++)
      if (ls[i]) fa[ls[i]] = i;
    for (int i = (1); i <= (n); i++)
      if (rs[i]) fa[rs[i]] = i;
    int rt = 0;
    for (int i = (1); i <= (n); i++)
      if (fa[i] == 0) rt = i;
    dfs(rt);
    cout << dp[rt][m] << endl;
    return 0;
  }
  