#include <bits/stdc++.h>
using namespace std;
template <class T>
inline T read() {
  T r = 0, f = 0;
  char c = getchar();
  while (!isdigit(c)) f |= c == '-', c = getchar();
  while (isdigit(c)) r = (r << 3) + (r << 1) + (c ^ 48), c = getchar();
  return f ? -r : r;
}
const long long N = 4005, INF = 1e9;
long long n, m, a[N];
long long sz[N], f[N][N];
long long stk[N], top, ch[N][2];
void dfs(long long u) {
  sz[u] = 1;
  for (long long k = 0; k < 2; ++k) {
    long long v = ch[u][k], val = a[v] - a[u];
    if (!v) continue;
    dfs(v);
    for (long long i = min(m, sz[u]); ~i; --i)
      for (long long j = sz[v]; ~j; --j)
        f[u][i + j] = max(f[u][i + j], f[u][i] + f[v][j] + val * j * (m - j));
    sz[u] += sz[v];
  }
}
signed main() {
  n = read<long long>(), m = read<long long>();
  for (long long i = 1; i <= n; ++i) {
    a[i] = read<long long>();
    long long k = top;
    while (k && a[stk[k]] > a[i]) --k;
    if (k) ch[stk[k]][1] = i;
    if (k < top) ch[i][0] = stk[k + 1];
    stk[++k] = i, top = k;
  }
  dfs(stk[1]);
  printf("%lld", f[stk[1]][m]);
  return 0;
}

### Prompt

In Cpp, your task is to solve 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;
template <class T>
inline T read() {
  T r = 0, f = 0;
  char c = getchar();
  while (!isdigit(c)) f |= c == '-', c = getchar();
  while (isdigit(c)) r = (r << 3) + (r << 1) + (c ^ 48), c = getchar();
  return f ? -r : r;
}
const long long N = 4005, INF = 1e9;
long long n, m, a[N];
long long sz[N], f[N][N];
long long stk[N], top, ch[N][2];
void dfs(long long u) {
  sz[u] = 1;
  for (long long k = 0; k < 2; ++k) {
    long long v = ch[u][k], val = a[v] - a[u];
    if (!v) continue;
    dfs(v);
    for (long long i = min(m, sz[u]); ~i; --i)
      for (long long j = sz[v]; ~j; --j)
        f[u][i + j] = max(f[u][i + j], f[u][i] + f[v][j] + val * j * (m - j));
    sz[u] += sz[v];
  }
}
signed main() {
  n = read<long long>(), m = read<long long>();
  for (long long i = 1; i <= n; ++i) {
    a[i] = read<long long>();
    long long k = top;
    while (k && a[stk[k]] > a[i]) --k;
    if (k) ch[stk[k]][1] = i;
    if (k < top) ch[i][0] = stk[k + 1];
    stk[++k] = i, top = k;
  }
  dfs(stk[1]);
  printf("%lld", f[stk[1]][m]);
  return 0;
}

```