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, raw_input().split())
a = map(int, raw_input().split())
ans = 10 ** 12
for p in combinations(range(n), k):
    p = list(p)[::-1]
    ma = 0
    res = 0
    for j in xrange(n):
        if p and j == p[-1]:
            if ma < a[j]:
                ma = a[j]
            else:
                res += ma + 1 - a[j]
                ma += 1
            p.pop()
        else:
            if ma < a[j]:
                ma = a[j]
    if ans > res:
        ans = res
print ans
