#include <bits/stdc++.h>
using namespace std;
const int MAXN = 4010;
int n, m;
int a[MAXN];
int siz[MAXN];
unsigned long long dp[MAXN][MAXN];
int solve(int l, int r, int fa) {
  if (l > r) return 0;
  int minn = a[l], pos = l;
  for (int i = l + 1; i <= r; ++i) {
    if (a[i] < minn) {
      minn = a[i], pos = i;
    }
  }
  int ls = solve(l, pos - 1, pos), rs = solve(pos + 1, r, pos);
  siz[pos] = siz[ls] + siz[rs] + 1;
  int val = a[pos] - a[fa];
  for (int i = 0; i <= siz[ls]; ++i) {
    for (int j = 0; j <= siz[rs]; ++j) {
      if (i + j <= m)
        dp[pos][i + j] =
            max(dp[pos][i + j],
                dp[ls][i] + dp[rs][j] + 1ull * (m - i - j) * (i + j) * val);
      if (i + j + 1 <= m)
        dp[pos][i + j + 1] = max(
            dp[pos][i + j + 1],
            dp[ls][i] + dp[rs][j] + 1ull * (m - i - j - 1) * (i + j + 1) * val);
    }
  }
  return pos;
}
int main() {
  scanf("%d%d", &n, &m);
  for (int i = 1; i <= n; ++i) scanf("%d", &a[i]);
  int root = solve(1, n, 0);
  printf("%llu\n", dp[root][m]);
}

### Prompt

Please create a solution in Cpp 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 MAXN = 4010;
int n, m;
int a[MAXN];
int siz[MAXN];
unsigned long long dp[MAXN][MAXN];
int solve(int l, int r, int fa) {
  if (l > r) return 0;
  int minn = a[l], pos = l;
  for (int i = l + 1; i <= r; ++i) {
    if (a[i] < minn) {
      minn = a[i], pos = i;
    }
  }
  int ls = solve(l, pos - 1, pos), rs = solve(pos + 1, r, pos);
  siz[pos] = siz[ls] + siz[rs] + 1;
  int val = a[pos] - a[fa];
  for (int i = 0; i <= siz[ls]; ++i) {
    for (int j = 0; j <= siz[rs]; ++j) {
      if (i + j <= m)
        dp[pos][i + j] =
            max(dp[pos][i + j],
                dp[ls][i] + dp[rs][j] + 1ull * (m - i - j) * (i + j) * val);
      if (i + j + 1 <= m)
        dp[pos][i + j + 1] = max(
            dp[pos][i + j + 1],
            dp[ls][i] + dp[rs][j] + 1ull * (m - i - j - 1) * (i + j + 1) * val);
    }
  }
  return pos;
}
int main() {
  scanf("%d%d", &n, &m);
  for (int i = 1; i <= n; ++i) scanf("%d", &a[i]);
  int root = solve(1, n, 0);
  printf("%llu\n", dp[root][m]);
}

```