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 long long inf = 1000000000000000000;
  const int N = 4005;
  int n, m;
  long long a[N], dp[N][N];
  inline int read() {
    int F = 1, ANS = 0;
    char C = getchar();
    while (C < '0' || C > '9') {
      if (C == '-') F = -1;
      C = getchar();
    }
    while (C >= '0' && C <= '9') {
      ANS = ANS * 10 + C - '0';
      C = getchar();
    }
    return F * ANS;
  }
  int st[N], ls[N], rs[N], rt = 1;
  long long lw[N], rw[N], size[N];
  void build() {
    int top = 0, tot = 0;
    for (int i = 1; i <= n; i++) {
      if (a[i] < a[rt]) rt = i;
      tot = top;
      while (tot && a[st[tot]] > a[i]) tot--;
      if (tot) rs[st[tot]] = i, rw[st[tot]] = a[i] - a[st[tot]];
      if (tot < top) ls[i] = st[tot + 1], lw[i] = a[st[tot + 1]] - a[i];
      st[++tot] = i;
      top = tot;
    }
  }
  void dfs(int u) {
    size[u] = 1;
    if (ls[u]) {
      dfs(ls[u]);
      for (int i = size[u]; i >= 0; i--) {
        for (long long j = size[ls[u]]; j >= 0; j--) {
          dp[u][i + j] =
              max(dp[u][i + j], dp[u][i] + dp[ls[u]][j] + j * (m - j) * lw[u]);
        }
      }
      size[u] += size[ls[u]];
    }
    if (rs[u]) {
      dfs(rs[u]);
      for (int i = size[u]; i >= 0; i--) {
        for (long long j = size[rs[u]]; j >= 0; j--) {
          dp[u][i + j] =
              max(dp[u][i + j], dp[u][i] + dp[rs[u]][j] + j * (m - j) * rw[u]);
        }
      }
      size[u] += size[rs[u]];
    }
  }
  int main() {
    n = read(), m = read();
    for (int i = 1; i <= n; i++) a[i] = read();
    build();
    dfs(rt);
    cout << dp[rt][m];
    return 0;
  }
  