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
import copy
n,k = map(int,input().split())
a = list(map(int,input().split()))

flag = 0
for i in range(2**n):
    state = bin(i)[2:]
    state = '0'*(n - len(state)) + state
    state = [int(i) for i in state]
    
    if sum(state)==k:
        a_state = copy.copy(a)
    
        cost = 0
        for j in range(n):
            if state[j]==1:
                cost_j = max(0,max([0]+a_state[:j])+1-a_state[j])
                cost += cost_j
                a_state[j] += cost_j
            
    
    
        if flag ==0:
            ans =cost
        flag+=1
        ans = min(ans,cost)
print(ans)