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;
using ll = long long;

int a[20];

int main()
{
    int n, k;
    cin >> n >> k;
    rep(i,n) cin >> a[i];

    ll ans = ll(1e18)+1;
    rep(bit,1<<n) {
        ll tot = 0;
        int maxv = 0;
        int visible = 0;
        rep(i,n) {
            if (maxv < a[i]) {
                visible++;
                maxv = a[i];
            } else if (bit>>i&1) {
                tot += (maxv - a[i]) + 1;
                visible++;
                maxv++;
            }
        }
        if (visible >= k) ans = min(ans, tot); 
    }
    cout << ans << endl;

    return 0;
}