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 long long read() {
    long long s = 0, f = 1;
    char _ch = getchar();
    while (!('0' <= _ch && _ch <= '9')) (_ch == '-') && (f = -1), _ch = getchar();
    while (('0' <= _ch && _ch <= '9')) s = s * 10 + _ch - 48, _ch = getchar();
    return s * f;
  }
  const long long N = 4010, inf = 1e17;
  long long n, m, a[N], stk[N], top, fa[N], ls[N], rs[N], sz[N];
  long long f[N][N];
  void dfs(long long x) {
    sz[x] = 1;
    if (ls[x]) {
      dfs(ls[x]);
      long long lm1 = min(sz[x], m), lm2;
      for (register long long i = lm1; i >= 0; i--) {
        lm2 = min(sz[ls[x]], m);
        for (register long long j = lm2; j >= 0; j--)
          f[x][i + j] =
              max(f[x][i + j],
                  f[x][i] + f[ls[x]][j] + 1ll * j * (m - j) * (a[ls[x]] - a[x]));
      }
      sz[x] += sz[ls[x]];
    }
    if (rs[x]) {
      dfs(rs[x]);
      long long lm1 = min(sz[x], m), lm2;
      for (register long long i = lm1; i >= 0; i--) {
        lm2 = min(sz[rs[x]], m);
        for (register long long j = lm2; j >= 0; j--)
          f[x][i + j] =
              max(f[x][i + j],
                  f[x][i] + f[rs[x]][j] + 1ll * j * (m - j) * (a[rs[x]] - a[x]));
      }
      sz[x] += sz[rs[x]];
    }
  }
  signed main() {
    n = read(), m = read();
    for (register long long i = 1; i <= n; i++) a[i] = read();
    for (register long long i = 1; i <= n; i++) {
      while (top && a[i] < a[stk[top]]) ls[i] = stk[top--];
      rs[stk[top]] = i;
      stk[++top] = i;
    }
    for (register long long i = 1; i <= n; i++) fa[ls[i]] = fa[rs[i]] = i;
    long long p = 1;
    for (register long long i = 1; i <= n; i++)
      if (a[i] < a[p]) p = i;
    dfs(p);
    cout << f[p][m] << '\n';
    return 0;
  }
  