#include <bits/stdc++.h>
using namespace std;
inline long long read() {
  long long x = 0, f = 1;
  char c = getchar();
  while (!isdigit(c)) {
    if (c == '-') f = -1;
    c = getchar();
  }
  while (isdigit(c)) {
    x = (x << 3) + (x << 1) + (c ^ 48);
    c = getchar();
  }
  return f == -1 ? ~x + 1 : x;
}
long long n, m;
long long a[4010];
long long ls[4010], rs[4010];
long long stk[4010], top;
void build() {
  for (long long i = 1; i <= n; ++i) {
    while (top && a[stk[top]] > a[i]) {
      rs[stk[top]] = ls[i], ls[i] = stk[top];
      --top;
    }
    if (top) rs[stk[top]] = i;
    stk[++top] = i;
  }
}
long long sz[4010], dp[4010][4010], tmp[4010];
void dfs(long long x) {
  sz[x] = 1;
  dp[x][1] = (m - 1) * a[x];
  if (ls[x]) {
    dfs(ls[x]);
    for (long long i = 0; i <= sz[x] + sz[ls[x]]; ++i) tmp[i] = 0;
    for (long long i = 0; i <= sz[x]; ++i) {
      for (long long j = 0; j <= sz[ls[x]]; ++j) {
        tmp[i + j] =
            max(tmp[i + j], dp[x][i] + dp[ls[x]][j] - 2 * i * j * a[x]);
      }
    }
    sz[x] += sz[ls[x]];
    for (long long i = 0; i <= sz[x]; ++i) dp[x][i] = tmp[i];
  }
  if (rs[x]) {
    dfs(rs[x]);
    for (long long i = 0; i <= sz[x] + sz[rs[x]]; ++i) tmp[i] = 0;
    for (long long i = 0; i <= sz[x]; ++i) {
      for (long long j = 0; j <= sz[rs[x]]; ++j) {
        tmp[i + j] =
            max(tmp[i + j], dp[x][i] + dp[rs[x]][j] - 2 * i * j * a[x]);
      }
    }
    sz[x] += sz[rs[x]];
    for (long long i = 0; i <= sz[x]; ++i) dp[x][i] = tmp[i];
  }
}
signed main() {
  n = read(), m = read();
  for (long long i = 1; i <= n; ++i) a[i] = read();
  build();
  dfs(stk[1]);
  printf("%lld\n", dp[stk[1]][m]);
}

### Prompt

Your challenge is to write a CPP solution 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;
inline long long read() {
  long long x = 0, f = 1;
  char c = getchar();
  while (!isdigit(c)) {
    if (c == '-') f = -1;
    c = getchar();
  }
  while (isdigit(c)) {
    x = (x << 3) + (x << 1) + (c ^ 48);
    c = getchar();
  }
  return f == -1 ? ~x + 1 : x;
}
long long n, m;
long long a[4010];
long long ls[4010], rs[4010];
long long stk[4010], top;
void build() {
  for (long long i = 1; i <= n; ++i) {
    while (top && a[stk[top]] > a[i]) {
      rs[stk[top]] = ls[i], ls[i] = stk[top];
      --top;
    }
    if (top) rs[stk[top]] = i;
    stk[++top] = i;
  }
}
long long sz[4010], dp[4010][4010], tmp[4010];
void dfs(long long x) {
  sz[x] = 1;
  dp[x][1] = (m - 1) * a[x];
  if (ls[x]) {
    dfs(ls[x]);
    for (long long i = 0; i <= sz[x] + sz[ls[x]]; ++i) tmp[i] = 0;
    for (long long i = 0; i <= sz[x]; ++i) {
      for (long long j = 0; j <= sz[ls[x]]; ++j) {
        tmp[i + j] =
            max(tmp[i + j], dp[x][i] + dp[ls[x]][j] - 2 * i * j * a[x]);
      }
    }
    sz[x] += sz[ls[x]];
    for (long long i = 0; i <= sz[x]; ++i) dp[x][i] = tmp[i];
  }
  if (rs[x]) {
    dfs(rs[x]);
    for (long long i = 0; i <= sz[x] + sz[rs[x]]; ++i) tmp[i] = 0;
    for (long long i = 0; i <= sz[x]; ++i) {
      for (long long j = 0; j <= sz[rs[x]]; ++j) {
        tmp[i + j] =
            max(tmp[i + j], dp[x][i] + dp[rs[x]][j] - 2 * i * j * a[x]);
      }
    }
    sz[x] += sz[rs[x]];
    for (long long i = 0; i <= sz[x]; ++i) dp[x][i] = tmp[i];
  }
}
signed main() {
  n = read(), m = read();
  for (long long i = 1; i <= n; ++i) a[i] = read();
  build();
  dfs(stk[1]);
  printf("%lld\n", dp[stk[1]][m]);
}

```