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;
using Int = long long;
int main() {
    cin.tie(nullptr); ios::sync_with_stdio(false);
    int N, K; cin >> N >> K;
    vector<Int> A(N); for (auto &a : A) cin >> a;
    Int ans = 1e18;
    for (int bits = 0; bits < (1 << N); bits++) {
        if (__builtin_popcount(bits) < K) continue;
        Int curr = 0, cost = 0;
        for (int i = 0; i < N; i++) {
            if (bits & (1 << i)) {
                int next = max(curr + 1, A[i]);
                cost += next - A[i];
                curr = next;
            } else {
                curr = max(curr, A[i]);
            }
        }
        ans = min(ans, cost);
    }
    cout << ans << endl;
    return 0;
}
