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
n, k = map(int, input().split())
pbls = list(map(int, input().split()))
ans = 1e18
for i in range(pow(2, n)):
    bls = pbls[::]
    if (bin(i).count("1") != k):
        continue
    temp = 0
    l = []
    for b in range(n):
        if (i & (1 << b)):
            l.append(b)
    for c in l:
        if (c == 0):
            continue
        else:
            m = max(bls[:c])
            if (m < bls[c]):
                pass
            else:
                temp += m + 1 - bls[c]
                bls[c] = m + 1
    ans = min(ans,temp)
print(ans)

