#include <bits/stdc++.h>
using namespace std;
int read();
const int N = 4005;
int n, m, st[N], top, ch[N][2], siz[N];
long long dp[N][N], a[N];
void dfs(int u) {
  if (!u) return;
  int lc = ch[u][0], rc = ch[u][1];
  dfs(lc);
  dfs(rc);
  siz[u] = siz[lc] + siz[rc] + 1;
  for (int i = (0); i <= (siz[lc]); ++i)
    for (int j = (0); j <= (siz[rc]); ++j) {
      dp[u][i + j] =
          max(dp[u][i + j], dp[lc][i] + dp[rc][j] - 2ll * i * j * a[u]);
      dp[u][i + j + 1] = max(
          dp[u][i + j + 1], dp[lc][i] + dp[rc][j] + m * a[u] -
                                2ll * i * j * a[u] - (i + j) * a[u] * 2 - a[u]);
    }
}
int main() {
  cin >> n >> m;
  for (int i = (1); i <= (n); ++i) cin >> a[i];
  for (int i = (1); i <= (n); ++i) {
    while (top && a[st[top]] > a[i]) ch[i][0] = st[top--];
    if (top) ch[st[top]][1] = i;
    st[++top] = i;
  }
  dfs(st[1]);
  cout << dp[st[1]][m] << endl;
  return 0;
}

### Prompt

Construct a CPP code solution to the problem outlined:

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].

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
int read();
const int N = 4005;
int n, m, st[N], top, ch[N][2], siz[N];
long long dp[N][N], a[N];
void dfs(int u) {
  if (!u) return;
  int lc = ch[u][0], rc = ch[u][1];
  dfs(lc);
  dfs(rc);
  siz[u] = siz[lc] + siz[rc] + 1;
  for (int i = (0); i <= (siz[lc]); ++i)
    for (int j = (0); j <= (siz[rc]); ++j) {
      dp[u][i + j] =
          max(dp[u][i + j], dp[lc][i] + dp[rc][j] - 2ll * i * j * a[u]);
      dp[u][i + j + 1] = max(
          dp[u][i + j + 1], dp[lc][i] + dp[rc][j] + m * a[u] -
                                2ll * i * j * a[u] - (i + j) * a[u] * 2 - a[u]);
    }
}
int main() {
  cin >> n >> m;
  for (int i = (1); i <= (n); ++i) cin >> a[i];
  for (int i = (1); i <= (n); ++i) {
    while (top && a[st[top]] > a[i]) ch[i][0] = st[top--];
    if (top) ch[st[top]][1] = i;
    st[++top] = i;
  }
  dfs(st[1]);
  cout << dp[st[1]][m] << endl;
  return 0;
}

```