#include <bits/stdc++.h>
using namespace std;
int n, m, sz[4010];
long long dp[4010][4010], a[4010];
int sol(int l, int r) {
  if (l > r) return 0;
  int id = l;
  for (int i = l + 1; i <= r; i++)
    if (a[id] > a[i]) id = i;
  int ls = sol(l, id - 1), rs = sol(id + 1, r);
  sz[id] = sz[ls] + sz[rs] + 1;
  for (int i = 0; i <= sz[ls]; i++)
    for (int j = 0; j <= sz[rs]; j++)
      dp[id][i + j] =
          max(dp[id][i + j], dp[ls][i] + dp[rs][j] - a[id] * i * j * 2);
  for (int i = sz[id]; i; i--)
    dp[id][i] = max(dp[id][i], dp[id][i - 1] + a[id] * (m - 2 * i + 1));
  return id;
}
int main() {
  memset(dp, -0x7f, sizeof(dp));
  dp[0][0] = 0;
  scanf("%d%d", &n, &m);
  for (int i = 1; i <= n; i++) scanf("%lld", &a[i]);
  int rt = sol(1, n);
  return printf("%lld", dp[rt][m]), 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 n, m, sz[4010];
long long dp[4010][4010], a[4010];
int sol(int l, int r) {
  if (l > r) return 0;
  int id = l;
  for (int i = l + 1; i <= r; i++)
    if (a[id] > a[i]) id = i;
  int ls = sol(l, id - 1), rs = sol(id + 1, r);
  sz[id] = sz[ls] + sz[rs] + 1;
  for (int i = 0; i <= sz[ls]; i++)
    for (int j = 0; j <= sz[rs]; j++)
      dp[id][i + j] =
          max(dp[id][i + j], dp[ls][i] + dp[rs][j] - a[id] * i * j * 2);
  for (int i = sz[id]; i; i--)
    dp[id][i] = max(dp[id][i], dp[id][i - 1] + a[id] * (m - 2 * i + 1));
  return id;
}
int main() {
  memset(dp, -0x7f, sizeof(dp));
  dp[0][0] = 0;
  scanf("%d%d", &n, &m);
  for (int i = 1; i <= n; i++) scanf("%lld", &a[i]);
  int rt = sol(1, n);
  return printf("%lld", dp[rt][m]), 0;
}

```