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;
  const int MAXN = 4005;
  const long long INF = 1e18;
  template <typename T>
  void chkmax(T& x, T y) {
    if (y > x) x = y;
  }
  template <typename T>
  void chkmin(T& x, T y) {
    if (y < x) x = y;
  }
  int N, M, a[MAXN], stk[MAXN], slen, ls[MAXN], rs[MAXN], rt;
  long long f[MAXN][MAXN];
  int siz[MAXN];
  void dfs(int u) {
    if (ls[u]) dfs(ls[u]);
    if (rs[u]) dfs(rs[u]);
    if (!ls[u] && !rs[u]) {
      f[u][0] = 0;
      f[u][1] = 1ll * (M - 1) * a[u];
      siz[u] = 1;
    } else {
      siz[u] = siz[ls[u]] + siz[rs[u]] + 1;
      for (int i = 1; i <= siz[u]; ++i) f[u][i] = -INF;
      for (int i = 0; i <= siz[ls[u]]; ++i)
        for (int j = 0; j <= siz[rs[u]]; ++j) {
          long long tmp = f[ls[u]][i] + f[rs[u]][j] - 2ll * a[u] * i * j;
          if (tmp > f[u][i + j]) f[u][i + j] = tmp;
          tmp = f[ls[u]][i] + f[rs[u]][j] - 2ll * a[u] * (i * j + i + j) +
                1ll * a[u] * (M - 1);
          if (tmp > f[u][i + j + 1]) f[u][i + j + 1] = tmp;
        }
    }
  }
  int main() {
    scanf("%d%d", &N, &M);
    for (int i = 1; i <= N; ++i) scanf("%d", &a[i]);
    for (int i = 1; i <= N; ++i) {
      while (slen && a[stk[slen]] > a[i]) ls[i] = stk[slen], --slen;
      rs[stk[slen]] = i, stk[++slen] = i;
    }
    rt = stk[1];
    dfs(rt);
    printf("%lld", f[rt][M]);
    return 0;
  }
  