#include <bits/stdc++.h>
using namespace std;
int n, m;
const int N = 4005;
int a[N], ls[N], rs[N], sz[N];
int st[N], tot;
long long lw[N], rw[N], f[N][N];
void dfs(int u) {
  int i, j;
  sz[u] = 1;
  if (ls[u]) {
    dfs(ls[u]);
    for (i = min(sz[u], m); i >= 0; i--)
      for (j = min(sz[ls[u]], m); j >= 0; j--)
        f[u][i + j] = max(f[u][i + j], f[ls[u]][j] + lw[u] * j * (m - j));
    sz[u] += sz[ls[u]];
  }
  if (rs[u]) {
    dfs(rs[u]);
    for (i = min(sz[u], m); i >= 0; i--)
      for (j = min(sz[rs[u]], m); j >= 0; j--)
        f[u][i + j] =
            max(f[u][i + j], f[u][i] + f[rs[u]][j] + rw[u] * j * (m - j));
    sz[u] += sz[rs[u]];
  }
}
int main() {
  int i;
  cin >> n >> m;
  for (i = 1; i <= n; i++) {
    scanf("%d", &a[i]);
    while (tot > 0 && a[st[tot]] > a[i])
      ls[i] = st[tot], lw[i] = a[st[tot]] - a[i], tot--;
    if (tot) rs[st[tot]] = i, rw[st[tot]] = a[i] - a[st[tot]];
    st[++tot] = i;
  }
  dfs(st[1]);
  cout << f[st[1]][m];
  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 n, m;
const int N = 4005;
int a[N], ls[N], rs[N], sz[N];
int st[N], tot;
long long lw[N], rw[N], f[N][N];
void dfs(int u) {
  int i, j;
  sz[u] = 1;
  if (ls[u]) {
    dfs(ls[u]);
    for (i = min(sz[u], m); i >= 0; i--)
      for (j = min(sz[ls[u]], m); j >= 0; j--)
        f[u][i + j] = max(f[u][i + j], f[ls[u]][j] + lw[u] * j * (m - j));
    sz[u] += sz[ls[u]];
  }
  if (rs[u]) {
    dfs(rs[u]);
    for (i = min(sz[u], m); i >= 0; i--)
      for (j = min(sz[rs[u]], m); j >= 0; j--)
        f[u][i + j] =
            max(f[u][i + j], f[u][i] + f[rs[u]][j] + rw[u] * j * (m - j));
    sz[u] += sz[rs[u]];
  }
}
int main() {
  int i;
  cin >> n >> m;
  for (i = 1; i <= n; i++) {
    scanf("%d", &a[i]);
    while (tot > 0 && a[st[tot]] > a[i])
      ls[i] = st[tot], lw[i] = a[st[tot]] - a[i], tot--;
    if (tot) rs[st[tot]] = i, rw[st[tot]] = a[i] - a[st[tot]];
    st[++tot] = i;
  }
  dfs(st[1]);
  cout << f[st[1]][m];
  return 0;
}

```