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>
typedef long long ll;
using namespace std;

int main() {
    int n, k;
    cin >> n >> k;
    vector<ll> a(n);
    for (int i = 0; i < n; ++i) {
        cin >> a[i];
    }
    ll ans = 1001001001001001001;
    for (int i = 0; i < (1 << n); ++i) {
        bitset<15> bs(i);
        ll highest = 0;
        ll cost = 0;
        vector<ll> copy = a;
        for (int j = 0; j < n; ++j) {
            if (bs.test(j) and copy[j] <= highest) {
                cost += highest - copy[j] + 1;
                copy[j] = highest + 1;
            }
            highest = max(highest, copy[j]);
        }
        int see = 0;
        highest = 0;
        for (int j = 0; j < n; ++j) {
            if (highest < copy[j]) {
                see++;
            }
            highest = max(highest, copy[j]);
        }
        if (see < k) continue;
        ans = min(ans, cost);
    }
    cout << ans << endl;
}