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>
  const long long mod = 998244353;
  long long Add(long long x, long long y) {
    return (x + y >= mod) ? (x + y - mod) : (x + y);
  }
  long long Mul(long long x, long long y) { return x * y % mod; }
  long long Mod(long long x) {
    return x < 0 ? (x + mod) : (x >= mod ? (x - mod) : x);
  }
  long long cadd(long long &x, long long y) {
    return x = (x + y >= mod) ? (x + y - mod) : (x + y);
  }
  template <typename T>
  T Max(T x, T y) {
    return x > y ? x : y;
  }
  template <typename T>
  T Min(T x, T y) {
    return x < y ? x : y;
  }
  template <typename T>
  T &read(T &r) {
    r = 0;
    bool w = 0;
    char ch = getchar();
    while (ch < '0' || ch > '9') w = ch == '-' ? 1 : 0, ch = getchar();
    while (ch >= '0' && ch <= '9') r = r * 10 + (ch ^ 48), ch = getchar();
    return r = w ? -r : r;
  }
  const long long N = 4010;
  long long n, m, ls[N], rs[N], st[N], top, a[N], siz[N];
  long long f[N][N];
  std::vector<long long> eg[N];
  void dfs(long long x) {
    siz[x] = 1;
    for (auto v : eg[x]) dfs(v);
    if (eg[x].size() == 0) {
      f[x][1] = 1ll * (m - 1) * a[x];
      return;
    }
    for (auto v : eg[x]) {
      for (long long j = siz[x] + siz[v]; j >= 0; --j)
        for (long long k = Max(0ll, j - siz[x]); k <= Min(j, siz[v]); ++k)
          f[x][j] =
              Max(f[x][j], f[v][k] + f[x][j - k] - 2ll * k * (j - k) * a[x]);
      siz[x] += siz[v];
    }
    for (long long j = siz[x]; j; --j)
      f[x][j] =
          Max(f[x][j], f[x][j - 1] + 1ll * (m - 1) * a[x] - 2ll * (j - 1) * a[x]);
  }
  signed main() {
    read(n);
    read(m);
    for (long long i = 1; i <= n; ++i)
      for (long long j = 1; j <= m; ++j) f[i][j] = -0x3f3f3f3f3f3f3f3f;
    for (long long i = 1; i <= n; ++i) {
      read(a[i]);
      long long k = top;
      while (k && a[st[k]] > a[i]) --k;
      if (k) rs[st[k]] = i;
      if (k < top) ls[i] = st[k + 1];
      st[top = k + 1] = i;
    }
    for (long long i = 1; i <= n; ++i) {
      if (ls[i]) eg[i].emplace_back(ls[i]);
      if (rs[i]) eg[i].emplace_back(rs[i]);
    }
    dfs(st[1]);
    printf("%lld\n", f[st[1]][m]);
    return 0;
  }
  