#include <bits/stdc++.h>
using namespace std;
const int N = 4010;
int a[N], ls[N], rs[N], sk[N], siz[N], m;
long long f[N][N];
void dfs(int x) {
  if (!x) return;
  dfs(ls[x]);
  dfs(rs[x]);
  siz[x] = siz[ls[x]] + siz[rs[x]] + 1;
  for (int i = 0; i <= siz[ls[x]]; i++)
    for (int j = 0; j <= siz[rs[x]]; j++) {
      f[x][i + j] =
          max(f[x][i + j], f[ls[x]][i] + f[rs[x]][j] - 2ll * i * j * a[x]);
      f[x][i + j + 1] =
          max(f[x][i + j + 1], f[ls[x]][i] + f[rs[x]][j] + 1ll * m * a[x] -
                                   (2ll * (i + 1) * (j + 1) - 1) * a[x]);
    }
}
signed main() {
  int n, top = 0;
  scanf("%d%d", &n, &m);
  for (int i = 1; i <= n; i++) {
    scanf("%d", a + i);
    int las = 0;
    while (top && a[i] <= a[sk[top]]) las = sk[top--];
    if (las) ls[i] = las;
    if (top) rs[sk[top]] = i;
    sk[++top] = i;
  }
  dfs(sk[1]);
  printf("%lld\n", f[sk[1]][m]);
  return 0;
}

### Prompt

Generate a Cpp solution to the following problem:

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;
const int N = 4010;
int a[N], ls[N], rs[N], sk[N], siz[N], m;
long long f[N][N];
void dfs(int x) {
  if (!x) return;
  dfs(ls[x]);
  dfs(rs[x]);
  siz[x] = siz[ls[x]] + siz[rs[x]] + 1;
  for (int i = 0; i <= siz[ls[x]]; i++)
    for (int j = 0; j <= siz[rs[x]]; j++) {
      f[x][i + j] =
          max(f[x][i + j], f[ls[x]][i] + f[rs[x]][j] - 2ll * i * j * a[x]);
      f[x][i + j + 1] =
          max(f[x][i + j + 1], f[ls[x]][i] + f[rs[x]][j] + 1ll * m * a[x] -
                                   (2ll * (i + 1) * (j + 1) - 1) * a[x]);
    }
}
signed main() {
  int n, top = 0;
  scanf("%d%d", &n, &m);
  for (int i = 1; i <= n; i++) {
    scanf("%d", a + i);
    int las = 0;
    while (top && a[i] <= a[sk[top]]) las = sk[top--];
    if (las) ls[i] = las;
    if (top) rs[sk[top]] = i;
    sk[++top] = i;
  }
  dfs(sk[1]);
  printf("%lld\n", f[sk[1]][m]);
  return 0;
}

```