#include <bits/stdc++.h>
void sc(int &x) { scanf("%d", &x); }
void sc(int &x, int &y) { scanf("%d%d", &x, &y); }
void sc(int &x, int &y, int &z) { scanf("%d%d%d", &x, &y, &z); }
void sc(long long &x) { scanf("%lld", &x); }
void sc(long long &x, long long &y) { scanf("%lld%lld", &x, &y); }
void sc(long long &x, long long &y, long long &z) {
  scanf("%lld%lld%lld", &x, &y, &z);
}
void sc(char *x) { scanf("%s", x); }
void sc(char *x, char *y) { scanf("%s%s", x, y); }
void sc(char *x, char *y, char *z) { scanf("%s%s%s", x, y, z); }
void out(int x) { printf("%d\n", x); }
void out(long long x) { printf("%lld\n", x); }
void out(int x, int y) { printf("%d %d\n", x, y); }
void out(long long x, long long y) { printf("%lld %lld\n", x, y); }
void out(int x, int y, int z) { printf("%d %d %d\n", x, y, z); }
void out(long long x, long long y, long long z) {
  printf("%lld %lld %lld\n", x, y, z);
}
void ast(long long x, long long l, long long r) { assert(x >= l && x <= r); }
using namespace std;
const int N = 4005;
int n, m, top, s[N], si[N], a[N], t[N][2];
long long dp[N][N], g[N];
void update(long long &x, long long y) {
  if (y > x) x = y;
}
void dfs(int u) {
  dp[u][0] = dp[u][1] = 0;
  si[u] = 1;
  int v = t[u][0];
  if (v) {
    dfs(v);
    memset(g, 0, sizeof(g));
    for (int i = 0; i <= si[u]; i++)
      for (int j = 0; j <= si[v] && i + j <= m; j++)
        update(g[i + j],
               dp[u][i] + dp[v][j] + 1ll * j * (m - j) * (a[v] - a[u]));
    memcpy(dp[u], g, sizeof(g));
    si[u] += si[v];
  }
  v = t[u][1];
  if (v) {
    dfs(v);
    memset(g, 0, sizeof(g));
    for (int i = 0; i <= si[u]; i++)
      for (int j = 0; j <= si[v] && i + j <= m; j++)
        update(g[i + j],
               dp[u][i] + dp[v][j] + 1ll * j * (m - j) * (a[v] - a[u]));
    memcpy(dp[u], g, sizeof(g));
    si[u] += si[v];
  }
}
void sol(int cas) {
  sc(n, m);
  for (int i = 1; i <= n; i++) sc(a[i]);
  for (int i = 1; i <= n; i++) {
    while (top && a[s[top]] > a[i]) {
      if (a[s[top - 1]] > a[i])
        t[s[top - 1]][1] = s[top];
      else
        t[i][0] = s[top];
      top--;
    }
    s[++top] = i;
  }
  while (top > 1) t[s[top - 1]][1] = s[top], top--;
  dfs(s[top]);
  printf("%lld\n", dp[s[top]][m]);
}
int main() {
  srand(time(0));
  int t = 1, cas = 0;
  while (t--) {
    sol(++cas);
  }
}

### Prompt

Create a solution in cpp for 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>
void sc(int &x) { scanf("%d", &x); }
void sc(int &x, int &y) { scanf("%d%d", &x, &y); }
void sc(int &x, int &y, int &z) { scanf("%d%d%d", &x, &y, &z); }
void sc(long long &x) { scanf("%lld", &x); }
void sc(long long &x, long long &y) { scanf("%lld%lld", &x, &y); }
void sc(long long &x, long long &y, long long &z) {
  scanf("%lld%lld%lld", &x, &y, &z);
}
void sc(char *x) { scanf("%s", x); }
void sc(char *x, char *y) { scanf("%s%s", x, y); }
void sc(char *x, char *y, char *z) { scanf("%s%s%s", x, y, z); }
void out(int x) { printf("%d\n", x); }
void out(long long x) { printf("%lld\n", x); }
void out(int x, int y) { printf("%d %d\n", x, y); }
void out(long long x, long long y) { printf("%lld %lld\n", x, y); }
void out(int x, int y, int z) { printf("%d %d %d\n", x, y, z); }
void out(long long x, long long y, long long z) {
  printf("%lld %lld %lld\n", x, y, z);
}
void ast(long long x, long long l, long long r) { assert(x >= l && x <= r); }
using namespace std;
const int N = 4005;
int n, m, top, s[N], si[N], a[N], t[N][2];
long long dp[N][N], g[N];
void update(long long &x, long long y) {
  if (y > x) x = y;
}
void dfs(int u) {
  dp[u][0] = dp[u][1] = 0;
  si[u] = 1;
  int v = t[u][0];
  if (v) {
    dfs(v);
    memset(g, 0, sizeof(g));
    for (int i = 0; i <= si[u]; i++)
      for (int j = 0; j <= si[v] && i + j <= m; j++)
        update(g[i + j],
               dp[u][i] + dp[v][j] + 1ll * j * (m - j) * (a[v] - a[u]));
    memcpy(dp[u], g, sizeof(g));
    si[u] += si[v];
  }
  v = t[u][1];
  if (v) {
    dfs(v);
    memset(g, 0, sizeof(g));
    for (int i = 0; i <= si[u]; i++)
      for (int j = 0; j <= si[v] && i + j <= m; j++)
        update(g[i + j],
               dp[u][i] + dp[v][j] + 1ll * j * (m - j) * (a[v] - a[u]));
    memcpy(dp[u], g, sizeof(g));
    si[u] += si[v];
  }
}
void sol(int cas) {
  sc(n, m);
  for (int i = 1; i <= n; i++) sc(a[i]);
  for (int i = 1; i <= n; i++) {
    while (top && a[s[top]] > a[i]) {
      if (a[s[top - 1]] > a[i])
        t[s[top - 1]][1] = s[top];
      else
        t[i][0] = s[top];
      top--;
    }
    s[++top] = i;
  }
  while (top > 1) t[s[top - 1]][1] = s[top], top--;
  dfs(s[top]);
  printf("%lld\n", dp[s[top]][m]);
}
int main() {
  srand(time(0));
  int t = 1, cas = 0;
  while (t--) {
    sol(++cas);
  }
}

```