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>
#define rep(i, n) for (int i=0; i<(n); i++)
#define ll long long
using namespace std;

int main() {
  int n,k; cin>>n>>k;
  vector<ll> A(n);
  rep(i, n) cin>>A[i];
  ll res=1e12;

  if (k==1) {
    cout<<0<<endl;
    return 0;
  }

  rep(bit, (1<<n)) {
     int tmp=0;
     rep(i, n) {
       if (bit&(1<<i)) tmp++;
     }
     if (tmp!=k) continue;
     ll sum=0;
     ll minH=A[0];
     for (int i=1; i<n; i++) {
       minH=max(minH, A[i]);
       if (bit&(1<<i)) {
         if (minH>=A[i]) {
           sum+=minH-A[i]+1;
           minH++;
         }
       }
     }
     res=min(res, sum);
  }
  cout<<res<<endl;
}