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++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include<bits/stdc++.h>
using namespace std;
int64_t f(vector<int64_t>a,int k){
int N=a.size();
  if(N<k)
  return 2000000000;
  else if(k==1){
  return 0;
  }else {
  if(a.at(0)<a.at(1)){
  a.erase(a.begin());
    return f(a,k-1);
  }else{
  int64_t t=a.at(0)+1-a.at(1);
    vector<int64_t>b=a;
    vector<int64_t>c=a;
    b.erase(b.begin());b.at(0)+=t; c.erase(c.begin()+1);
    return min(t+f(b,k-1),f(c,k));
  }
  
  }

}
int main(){
int N,K;
  cin>>N>>K;
  vector<int64_t>a(N);
  for(int i=0;i<N;i++)
    cin>>a.at(i);
  int64_t ans=f(a,K);
  cout<<ans<<endl;
   return 0;
}