#include <bits/stdc++.h>
long long read(long long x = 0, long long f = 0, char ch = getchar()) {
  while (ch < 48 or ch > 57) f = ch == 45, ch = getchar();
  while (48 <= ch and ch <= 57) x = x * 10 + ch - 48, ch = getchar();
  return f ? -x : x;
}
const long long N = 1e6 + 5;
long long n, m, a[N];
std::vector<long long> solve(long long L, long long R) {
  std::vector<long long> res(R - L + 2, -1LL << 60);
  res[0] = 0;
  if (L > R) return res;
  long long pos = std::min_element(a + L, a + R + 1) - a;
  std::vector<long long> x = solve(L, pos - 1), y = solve(pos + 1, R);
  for (long long i = 0; i < x.size(); i++)
    for (long long j = 0; j < y.size(); j++) {
      res[i + j] = std::max(res[i + j], x[i] + y[j] - 2 * i * j * a[pos]);
      res[i + j + 1] = std::max(
          res[i + j + 1],
          x[i] + y[j] - (2 * (i + 1) * (j + 1) - 1) * a[pos] + m * a[pos]);
    }
  return res;
}
signed main() {
  n = read(), m = read();
  for (long long i = 1; i <= n; i++) a[i] = read();
  printf("%lld", solve(1, n)[m]);
  return 0;
}

### Prompt

Develop a solution in CPP to the problem described below:

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>
long long read(long long x = 0, long long f = 0, char ch = getchar()) {
  while (ch < 48 or ch > 57) f = ch == 45, ch = getchar();
  while (48 <= ch and ch <= 57) x = x * 10 + ch - 48, ch = getchar();
  return f ? -x : x;
}
const long long N = 1e6 + 5;
long long n, m, a[N];
std::vector<long long> solve(long long L, long long R) {
  std::vector<long long> res(R - L + 2, -1LL << 60);
  res[0] = 0;
  if (L > R) return res;
  long long pos = std::min_element(a + L, a + R + 1) - a;
  std::vector<long long> x = solve(L, pos - 1), y = solve(pos + 1, R);
  for (long long i = 0; i < x.size(); i++)
    for (long long j = 0; j < y.size(); j++) {
      res[i + j] = std::max(res[i + j], x[i] + y[j] - 2 * i * j * a[pos]);
      res[i + j + 1] = std::max(
          res[i + j + 1],
          x[i] + y[j] - (2 * (i + 1) * (j + 1) - 1) * a[pos] + m * a[pos]);
    }
  return res;
}
signed main() {
  n = read(), m = read();
  for (long long i = 1; i <= n; i++) a[i] = read();
  printf("%lld", solve(1, n)[m]);
  return 0;
}

```