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;
  char _c;
  bool _f;
  template <class T>
  inline void IN(T& x) {
    x = 0, _f = 0;
    while (_c = getchar(), !isdigit(_c))
      if (_c == '-') _f = 1;
    while (isdigit(_c)) x = x * 10 + _c - '0', _c = getchar();
    if (_f) x = -x;
  }
  template <class T>
  inline void chkmin(T& x, T y) {
    if (x > y) x = y;
  }
  template <class T>
  inline void chkmax(T& x, T y) {
    if (x < y) x = y;
  }
  const int N = 4e3 + 5;
  long long g[N], f[N][N];
  int n, m, top, a[N], lc[N], rc[N], sta[N], siz[N];
  void dfs(int u) {
    f[u][0] = 0, f[u][1] = 1ll * (m - 1) * a[u], siz[u] = 1;
    if (lc[u]) {
      dfs(lc[u]);
      memset(g, -63, sizeof g);
      for (int i = 0; i <= siz[lc[u]]; ++i)
        for (int j = 0; j <= siz[u]; ++j)
          chkmax(g[i + j], f[lc[u]][i] + f[u][j] - 2ll * i * j * a[u]);
      siz[u] += siz[lc[u]];
      for (int i = 0; i <= siz[u]; ++i) f[u][i] = g[i];
    }
    if (rc[u]) {
      dfs(rc[u]);
      memset(g, -63, sizeof g);
      for (int i = 0; i <= siz[rc[u]]; ++i)
        for (int j = 0; j <= siz[u]; ++j)
          chkmax(g[i + j], f[rc[u]][i] + f[u][j] - 2ll * i * j * a[u]);
      siz[u] += siz[rc[u]];
      for (int i = 0; i <= siz[u]; ++i) f[u][i] = g[i];
    }
  }
  int main() {
    IN(n), IN(m);
    for (int i = 1; i <= n; ++i) IN(a[i]);
    for (int i = 1; i <= n; ++i) {
      bool flag = false;
      while (top && a[sta[top]] > a[i]) --top, flag = true;
      rc[sta[top]] = i;
      if (flag) lc[i] = sta[top + 1];
      sta[++top] = i;
    }
    memset(f, -63, sizeof f), dfs(sta[1]);
    printf("%lld\n", f[sta[1]][m]);
    return 0;
  }
  