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
from itertools import combinations
N, K = map(int, input().split())
A = list(map(int, input().split()))

def f(p):
    ret = 0
    ma = 0
    for i, a in enumerate(A):
        if p[i] == 1:
            if ma == 0:
                pass
            else:
                if ma >= a:
                    ret += ma - a + 1
                    ma += 1
        ma = max(ma, a)
    return ret

ans = 10 ** 20
for comb in combinations(range(N), K):
    p = [1 if i in comb else 0 for i in range(N)]
    #if sum(p) < K: continue
    #print(p)
    ans = min(ans, f(p))

print(ans)

