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;
  inline void read(int &x) {
    char c;
    int f = 1;
    while (!isdigit(c = getchar()))
      if (c == '-') f = -1;
    x = (c & 15);
    while (isdigit(c = getchar())) x = (x << 1) + (x << 3) + (c & 15);
    x *= f;
  }
  int n, m, i, j, a[4005], sz[4005];
  int stk[4005], tp, lc[4005], rc[4005];
  long long f[4005][4005], g[4005];
  vector<int> bi[4005];
  void dfs(int x, int fa) {
    memset(f[x], -0x3f, sizeof(f[x]));
    f[x][0] = 0;
    f[x][1] = 1ll * (m - 1) * a[x];
    sz[x] = 1;
    for (__typeof((bi[x]).begin()) it = (bi[x]).begin(); it != (bi[x]).end();
         ++it) {
      dfs(*it, x);
      memset(g, -0x3f, sizeof(g));
      int i, j;
      for ((i) = 0; (i) <= (sz[x]); (i)++)
        for ((j) = 0; (j) <= (sz[*it]); (j)++) {
          g[i + j] = max(g[i + j], f[x][i] + f[*it][j] - 2ll * i * j * a[x]);
        }
      memcpy(f[x], g, sizeof(f[x]));
      sz[x] += sz[*it];
    }
  }
  int main() {
    read(n);
    read(m);
    for ((i) = 1; (i) <= (n); (i)++) read(a[i]);
    for ((i) = 1; (i) <= (n); (i)++) {
      int lst = 0;
      while (tp && a[stk[tp]] >= a[i]) {
        lst = stk[tp--];
      }
      lc[i] = lst;
      if (tp) rc[stk[tp]] = i;
      stk[++tp] = i;
    }
    int rt = stk[1];
    for ((i) = 1; (i) <= (n); (i)++) {
      if (lc[i]) bi[i].push_back(lc[i]);
      if (rc[i]) bi[i].push_back(rc[i]);
    }
    dfs(rt, 0);
    cout << f[rt][m] << endl;
    return 0;
  }
  