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.

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.

Input Format


N K
a_1 a_2 a_3 ... a_N

Example

Input

5 5
3949 3774 3598 3469 3424


Output

1541
#include <bits/stdc++.h>
using namespace std;

const int64_t INF = 1e18;

int main() {
    int N, K; cin >> N >> K;
    vector<int64_t> A(N);
    K--;
    for(auto &a : A) cin >> a;
    int64_t ans = INF;
    for(int bit = 0; bit < (1 << (N - 1)); ++bit) {
        if(__builtin_popcount(bit) != K) continue;
        int64_t now = A[0], cost = 0;
        for(int i = 1; i < N; ++i) {
            if(bit & (1 << (i - 1))) {
                int64_t dif = A[i] - now;
                if(dif > 0) {
                    now = A[i];
                } else {
                    cost += -dif + 1;
                    now = A[i] - dif + 1;
                }
            } else {
                now = max(now, A[i]);
            }
        }
        ans = min(ans, cost);
    }
    cout << ans << '\n';
    return 0;
}
