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()))

ans = 10**12
for b in range(1<<n):
    c = 0
    for i in range(n):
        if ((b>>i)&1) == 1:
            c += 1
    if c != k: continue
    t = 0
    h = 0
    for i in range(n):
        if ((b>>i)&1) == 0:
            h = max(h, a[i])
            continue
        if h < a[i]:
            h = a[i]
            continue
        if h >= a[i]:
            t += h - a[i] + 1
            h += 1
            continue
    ans = min(ans, t)
print(ans)
