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
# B - Buildings are Colorful!
# 全探索、BIT全探索
N, K = map(int, input().split())
A = list(int(x) for x in input().split())

def solve(idx):
    ret = 0
    tmpmax = A[0]
    for i in range(1, idx[-1]+1):
        if A[i] <= tmpmax:
            if i in idx:
                ret += tmpmax - A[i] + 1
                tmpmax += 1
        else:
            tmpmax = A[i]
    return ret

ans = 10**18
for i in range(1<<N):
    idx = []
    for j in range(N):
        if i>>j&1:
            idx.append(j)
    if len(idx)==K and idx[0]==0:
        ans = min(ans, solve(idx))

print(ans)