Problem:
Max Score: 350 Points

Problem Statement

There are N buildings along the line. The i-th building from the left is colored in color i, and its height is currently a_i meters.

Chokudai is a mayor of the city, and he loves colorful thigs. And now he wants to see at least K buildings from the left.

You can increase height of buildings, but it costs 1 yens to increase 1 meters. It means you cannot make building that height is not integer.

You cannot decrease height of buildings.

Calculate the minimum cost of satisfying Chokudai's objective.

Note: "Building i can see from the left" means there are no j exists that (height of building j) ≥ (height of building i) and j < i.

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.

Sample Input 1

5 5
3949 3774 3598 3469 3424

Sample Output 1

1541

The optimal solution is (height of buildings from the left) = [3949, 3950, 3951, 3952, 3953].

Sample Input 2

5 3
7 4 2 6 4

Sample Output 2

7

The optimal solution is (height of buildings from the left) = [7, 8, 2, 9, 4].

Solution in C++ (GCC 9.2.1) (judge verdict: Wrong Answer)

#include<bits/stdc++.h>
using namespace std;
#define int int64_t
signed main(){
  int n,k,a[100],sum,ans=-1,ma,q;
  cin>>n>>k;
  for(int i=0;i<n;i++){
    cin>>a[i];
  }
  for(int i=0;i<(1<<(n));i++){
    sum=0;
    q=1;
    for(int j=0;j<n;j++){
      if(j==0) ma=a[0];
      if(i&(1<<j)&&j!=0){
	if(ma>=a[j]){
	  sum+=abs(a[j]-(ma+1));
	  ma+=1;
	  q++;
	}
	else q++;
      }
      else{
	if(ma<a[j]){
	  q++;
	  ma=a[j];
	}
      }
    }
    //cout<<q<<"\n";
    if(ans==-1&&q>=k) ans=sum;
    if(q>=k) ans=min(ans,sum);
  }
  cout<<ans<<"\n";
}