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())
a = list(map(int, input().split()))

res = 1<<60
for i in range(1<<n):    
    if i % 2 == 0: continue

    use_idx = [0 for _ in range(n)]
    use_cnt = 0
    for j in range(n):
        if i & (1<<j):
            use_idx[j] = 1
            use_cnt += 1
    
    if use_cnt != k: continue

    sm = 0
    mx = a[0]
    for j in range(1, n):
        if use_idx[j]:
            if a[j] <= mx:
                sm += mx+1 - a[j]
                mx += 1
        mx = max(mx, a[j])
    
    res = min(res, sm)

print(res)