#include <bits/stdc++.h>
using namespace std;
const int MAXN = 4005;
const long long INF = 1ll << 60;
int n, m, a[MAXN];
long long f[MAXN][MAXN];
int Dfs(int l, int r) {
  if (l > r) return 0;
  if (l == r) {
    f[l][0] = 0;
    f[l][1] = (m - 1ll) * a[l];
    return l;
  }
  int w = l;
  for (int i = l + 1; i <= r; i++)
    if (a[i] < a[w]) w = i;
  long long *f1 = f[Dfs(l, w - 1)], *f2 = f[Dfs(w + 1, r)];
  for (int i = 1; i <= r - l + 1; i++) f[w][i] = -INF;
  int l1 = w - l, l2 = r - w;
  for (int i = 0; i <= l1; i++)
    for (int j = 0; j <= l2; j++)
      f[w][i + j] = max(f[w][i + j], f1[i] + f2[j] - 2ll * i * j * a[w]);
  for (int i = r - l + 1; i; i--)
    f[w][i] = max(f[w][i], f[w][i - 1] + a[w] * (m + 1ll - i * 2));
  return w;
}
int main() {
  scanf("%d%d", &n, &m);
  for (int i = 1; i <= n; i++) scanf("%d", a + i);
  printf("%lld\n", f[Dfs(1, n)][m]);
  return 0;
}

### Prompt

Create a solution in cpp for 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 MAXN = 4005;
const long long INF = 1ll << 60;
int n, m, a[MAXN];
long long f[MAXN][MAXN];
int Dfs(int l, int r) {
  if (l > r) return 0;
  if (l == r) {
    f[l][0] = 0;
    f[l][1] = (m - 1ll) * a[l];
    return l;
  }
  int w = l;
  for (int i = l + 1; i <= r; i++)
    if (a[i] < a[w]) w = i;
  long long *f1 = f[Dfs(l, w - 1)], *f2 = f[Dfs(w + 1, r)];
  for (int i = 1; i <= r - l + 1; i++) f[w][i] = -INF;
  int l1 = w - l, l2 = r - w;
  for (int i = 0; i <= l1; i++)
    for (int j = 0; j <= l2; j++)
      f[w][i + j] = max(f[w][i + j], f1[i] + f2[j] - 2ll * i * j * a[w]);
  for (int i = r - l + 1; i; i--)
    f[w][i] = max(f[w][i], f[w][i - 1] + a[w] * (m + 1ll - i * 2));
  return w;
}
int main() {
  scanf("%d%d", &n, &m);
  for (int i = 1; i <= n; i++) scanf("%d", a + i);
  printf("%lld\n", f[Dfs(1, n)][m]);
  return 0;
}

```