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>
#define rep(i,n) for(int i = 0;i < n;i++)
using namespace std;
typedef long long int ll;
int main() {
    ll n, m,ans = 1e18; cin >> n >> m;
    vector<ll> a(n); rep(i, n) cin >> a[i];
    rep(i, 1 << n) {
        ll mx = 0, sum = 0, cnt = 0;
        rep(j, n) {
            if (i & (1 << j)) {
                cnt++;
                if (mx >= a[j]) sum += mx - a[j] + 1,mx++;
            }mx = max(mx, a[j]);
        }
        if (cnt >= m) ans = min(ans, sum);
    }cout << ans << endl;
}