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 = float('inf')
for b in range(1<<(N-1)):
    mxa = A[0]
    k = 1
    cost = 0
    for i,a in enumerate(A[1:]):
        if b&(1<<i):
            c = max(0, mxa+1 - a)
            cost += c
            mxa = max(a, mxa+1)
            k += 1
        else:
            if mxa < a:
                mxa = a
                k += 1
    if k >= K:
        ans = min(ans, cost)
print(ans)