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)