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;
  long long dp[Maxn][Maxn];
  int n, m;
  int a[Maxn];
  int sta[Maxn], top = 0;
  int ls[Maxn], rs[Maxn], siz[Maxn];
  int lw[Maxn], rw[Maxn];
  inline int read() {
    int x = 0, f = 1;
    char p = getchar();
    while (p < '0' || p > '9') {
      if (p == '-') f = -1;
      p = getchar();
    }
    while (p >= '0' && p <= '9') {
      x = (x << 1) + (x << 3) + p - '0';
      p = getchar();
    }
    return x * f;
  }
  void dfs(int x) {
    siz[x] = 1;
    if (ls[x]) {
      dfs(ls[x]);
      for (int i = min(siz[x], m); i >= 0; i--) {
        for (int j = min(siz[ls[x]], m); j >= 0; j--) {
          dp[x][i + j] = max(dp[x][i + j],
                             dp[x][i] + dp[ls[x]][j] + 1ll * j * (m - j) * lw[x]);
        }
      }
      siz[x] += siz[ls[x]];
    }
    if (rs[x]) {
      dfs(rs[x]);
      for (int i = min(siz[x], m); i >= 0; i--) {
        for (int j = min(siz[rs[x]], m); j >= 0; j--) {
          dp[x][i + j] = max(dp[x][i + j],
                             dp[x][i] + dp[rs[x]][j] + 1ll * j * (m - j) * rw[x]);
        }
      }
      siz[x] += siz[rs[x]];
    }
  }
  int main() {
    n = read(), m = read();
    for (int i = 1; i <= n; i++) {
      a[i] = read();
      int k = top;
      while (k > 0 && a[sta[k]] > a[i]) k--;
      if (k) rs[sta[k]] = i, rw[sta[k]] = a[i] - a[sta[k]];
      if (k < top) ls[i] = sta[k + 1], lw[i] = a[sta[k + 1]] - a[i];
      sta[++k] = i;
      top = k;
    }
    dfs(sta[1]);
    printf("%lld\n", dp[sta[1]][m]);
  }
  