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>
  template <class T>
  bool chmax(T &a, const T &b) {
    if (a < b) {
      a = b;
      return 1;
    }
    return 0;
  }
  template <class T>
  bool chmin(T &a, const T &b) {
    if (b < a) {
      a = b;
      return 1;
    }
    return 0;
  }
  using namespace std;
  string to_string(const string &s) { return '"' + s + '"'; }
  string to_string(const char *s) { return to_string((string)s); }
  template <typename A, typename B>
  string to_string(pair<A, B> p) {
    return "(" + to_string(p.first) + ", " + to_string(p.second) + ")";
  }
  void debug_out() { cerr << endl; }
  template <typename Head, typename... Tail>
  void debug_out(Head H, Tail... T) {
    cerr << " " << to_string(H);
    debug_out(T...);
  }
  using ll = long long;
  using LL = __int128;
  using pii = pair<int, int>;
  using vi = vector<int>;
  using db = double;
  using ldb = long double;
  const int maxn = 4000;
  const int mod = 1000000007;
  const int inf = 0x3f3f3f3f;
  ll a[maxn + 5];
  ll dp[maxn + 5][maxn + 5];
  int solve(int l, int r, int m) {
    if (l > r) return 0;
    ll mn = a[l];
    int mid = l;
    for (auto i = l + 1; i <= r; i++)
      if (chmin(mn, a[i])) mid = i;
    int ls = solve(l, mid - 1, m);
    int rs = solve(mid + 1, r, m);
    int L = mid - l, R = r - mid;
    for (auto x = 0; x <= L; x++)
      for (auto y = 0; y <= R; y++) {
        ll tmp = dp[ls][x] + dp[rs][y] + 1ll * x * (m - x) * (a[ls] - a[mid]) +
                 1ll * y * (m - y) * (a[rs] - a[mid]);
        chmax(dp[mid][x + y], tmp);
        chmax(dp[mid][x + y + 1], tmp);
      }
    return mid;
  }
  int main() {
    int n, m;
    scanf("%d%d", &n, &m);
    for (auto i = 1; i <= n; i++) scanf("%lld", &a[i]);
    printf("%lld\n", dp[solve(1, n, m)][m]);
    return 0;
  }
  