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>

using namespace std;
long long a[20],ans = 10000000000000000;
int main(){
	int i,j,n,k;
	cin >> n >> k;
	for(i=0;i<n;i++){
		cin >> a[i];
	}
	for(i=0;i<(1<<n);i++){
		if(__builtin_popcount(i)!=k) continue;
		long long h = 0,res = 0;
		for(j=0;j<n;j++){
			h = max(h,a[j]);
			if(!((1<<j)&i)) continue;
			if(a[j]<h){
				res += h + 1 - a[j];
				h++;
			}else{
				h = a[j];
			}
		}
		ans = min(ans,res);
	}
	cout << ans << endl;
}