#include <bits/stdc++.h>
using namespace std;
typedef long long ll;

int main(){
  int N, K; cin >> N >> K;
  vector<ll> a(N);
  for(int i = 0; i < N; i++){
    cin >> a[i];
  }
  ll ans = 1e18;
  for(int i = 0; i <1<<(N - 1); i++){
    bitset<18> bit(i);
    if(bit.count() != K-1)continue;
    ll ans1 = 0;
    ll bound = a[0];
    for(int j = 0; j < N - 1; j++){
      if(bit[j]){
        if(bound >= a[j + 1]){
          ans1 += bound - a[j + 1] + 1;
          bound++;
        }
        else{
          bound = a[j + 1];
        }
      }
      else{
        bound = max(bound, a[j + 1]);
      }
    }
    ans = min(ans, ans1);
  }
  cout << ans << endl;
}
### Prompt

Construct a cpp code solution to the problem outlined:

Input Format


N K
a_1 a_2 a_3 ... a_N


Output Format

Print the minimum cost in one line. In the end put a line break.


Constraints

* 1 ≤ K ≤ N ≤ 15
* 1 ≤ a_i ≤ 10^9



Scoring

Subtask 1 [120 points]


* N = K

Subtask 2 [90 points]


* N ≤ 5
* a_i ≤ 7

Subtask 3 [140 points]


* There are no additional constraints.

Output Format

Print the minimum cost in one line. In the end put a line break.


Constraints

* 1 ≤ K ≤ N ≤ 15
* 1 ≤ a_i ≤ 10^9



Scoring

Subtask 1 [120 points]


* N = K

Subtask 2 [90 points]


* N ≤ 5
* a_i ≤ 7

Subtask 3 [140 points]


* There are no additional constraints.

Input Format


N K
a_1 a_2 a_3 ... a_N

Example

Input

5 5
3949 3774 3598 3469 3424


Output

1541

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;

int main(){
  int N, K; cin >> N >> K;
  vector<ll> a(N);
  for(int i = 0; i < N; i++){
    cin >> a[i];
  }
  ll ans = 1e18;
  for(int i = 0; i <1<<(N - 1); i++){
    bitset<18> bit(i);
    if(bit.count() != K-1)continue;
    ll ans1 = 0;
    ll bound = a[0];
    for(int j = 0; j < N - 1; j++){
      if(bit[j]){
        if(bound >= a[j + 1]){
          ans1 += bound - a[j + 1] + 1;
          bound++;
        }
        else{
          bound = a[j + 1];
        }
      }
      else{
        bound = max(bound, a[j + 1]);
      }
    }
    ans = min(ans, ans1);
  }
  cout << ans << endl;
}
```