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<iostream>
#include<vector>
#include<algorithm>
#include<map>
#include<cstring>
#include<math.h>
#include<bitset>
#include<queue>
#include<set>
#include<iomanip>
#include<assert.h>
#include<string>
#include<cstdlib>
#include<cctype>
#include<unordered_map>
#include<sstream>
#include<numeric>
#include<stack>
// #include<bits/stdc++.h>
using namespace std;
using ll = long long;
using P = pair<int,int>;
constexpr ll INF = 9e18;
constexpr int inf = 1e9;
const double INFD = 1e100;
const ll mod = 1000000007;
const double PI = 3.1415926535897932384626433832795028841971;
const int dx[4] = {1, 0, -1, 0};
const int dy[4] = {0, 1, 0, -1};
template<class T> inline bool chmin(T& a, T b) {
    if (a > b) {
        a = b;
        return true;
    }
    return false;
};
template<class T> inline bool chmax(T& a, T b) {
    if (a < b) {
        a = b;
        return true;
    }
    return false;
};

// intやllをstringに変換
template<typename T> inline string toString(const T &a){
  ostringstream oss;
  oss << a;
  return oss.str();
};
// ----------------------------------------------------------------------------


int main(){
  ll N,K;
  cin >> N >> K;
  vector<ll> H(N);
  for(ll i=0; i<N; i++){
    cin >> H[i];
  }
  ll ans = INF;
  for(ll bit=0; bit<(1<<N); bit++){
    if(__builtin_popcount(bit) < K) continue;
    ll sum = 0;
    vector<ll> temp;
    temp = H;
    for(ll i=0; i<N; i++){
      if(bit & (1<<i)){
          ll h = temp[i];
          for(ll j=0; j<i; j++){
            chmax(h,temp[j]);
          }
          if(h != temp[i]){
            temp[i] = h+1;
          }
          sum += temp[i] - H[i];
      }
    }
    chmin(ans,sum);
  }
  cout << ans << endl;
  return 0;
}