#include <bits/stdc++.h>
using namespace std;
long long read() {
  long long x = 0, b = 1;
  char c;
  do c = getchar();
  while ((c > '9' || c < '0') && c != '-');
  if (c == '-') b = 0;
  do x = x * 10 + c - '0', c = getchar();
  while (c >= '0' && c <= '9');
  return b ? x : -x;
}
const long long maxn = 4010;
long long i, j, k, n, m, T, a[maxn], son[maxn][2], root, cnt, dp[maxn][maxn],
    size[maxn];
void dfs(long long &root, long long L, long long R) {
  if (L > R) return;
  if (!root) root = ++cnt;
  long long Min = L;
  for (long long i = L; i <= R; i++)
    if (a[i] < a[Min]) Min = i;
  dfs(son[root][0], L, Min - 1);
  dfs(son[root][1], Min + 1, R);
  size[root] = size[son[root][0]] + size[son[root][1]] + 1;
  for (long long i = 0; i <= size[son[root][0]]; i++)
    for (long long j = 0; j <= size[son[root][1]]; j++) {
      dp[root][i + j] =
          max(dp[root][i + j],
              dp[son[root][0]][i] + dp[son[root][1]][j] - 2 * i * j * a[Min]);
      dp[root][i + j + 1] =
          max(dp[root][i + j + 1],
              dp[son[root][0]][i] + dp[son[root][1]][j] + m * a[Min] -
                  (2 * i * j + 2 * i + 2 * j + 1) * a[Min]);
    }
}
signed main() {
  cin >> n >> m;
  for (i = 1; i <= n; i++) a[i] = read();
  dfs(root, 1, n);
  long long Ans = 0;
  cout << dp[root][m] << endl;
}

### 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;
long long read() {
  long long x = 0, b = 1;
  char c;
  do c = getchar();
  while ((c > '9' || c < '0') && c != '-');
  if (c == '-') b = 0;
  do x = x * 10 + c - '0', c = getchar();
  while (c >= '0' && c <= '9');
  return b ? x : -x;
}
const long long maxn = 4010;
long long i, j, k, n, m, T, a[maxn], son[maxn][2], root, cnt, dp[maxn][maxn],
    size[maxn];
void dfs(long long &root, long long L, long long R) {
  if (L > R) return;
  if (!root) root = ++cnt;
  long long Min = L;
  for (long long i = L; i <= R; i++)
    if (a[i] < a[Min]) Min = i;
  dfs(son[root][0], L, Min - 1);
  dfs(son[root][1], Min + 1, R);
  size[root] = size[son[root][0]] + size[son[root][1]] + 1;
  for (long long i = 0; i <= size[son[root][0]]; i++)
    for (long long j = 0; j <= size[son[root][1]]; j++) {
      dp[root][i + j] =
          max(dp[root][i + j],
              dp[son[root][0]][i] + dp[son[root][1]][j] - 2 * i * j * a[Min]);
      dp[root][i + j + 1] =
          max(dp[root][i + j + 1],
              dp[son[root][0]][i] + dp[son[root][1]][j] + m * a[Min] -
                  (2 * i * j + 2 * i + 2 * j + 1) * a[Min]);
    }
}
signed main() {
  cin >> n >> m;
  for (i = 1; i <= n; i++) a[i] = read();
  dfs(root, 1, n);
  long long Ans = 0;
  cout << dp[root][m] << endl;
}

```