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: Accepted)

#include<bits/stdc++.h>
using namespace std;
int main(){
    int N,K;scanf("%d%d",&N,&K);
    long long a[N];
    for(int i=0;i<N;i++)scanf("%lld",&a[i]);
    long long ans=1000000000000000;
    for(long long bit=0;bit<(1<<N);bit++){
        if(__builtin_popcount(bit)<K)continue;
        long long height=0,now=0;
        for(long long i=0;i<N;i++){
            if(bit&(1<<i)){
                if(height>=a[i]){
                    now+=height+1-a[i];
                    height++;
                }
                else height=a[i];
            }
            height=max(height,a[i]);
        }
        ans=min(ans,now);
    }
    printf("%lld\n",ans);
    return 0;
}