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
# square869120Contest #4
# B - Buildings are Colorful!
# https://atcoder.jp/contests/s8pc-4/tasks/s8pc_4_b
N, K = map(int, input().split())
*A, = map(int, input().split())

ans = float('inf')
for bit in range(2**N):
    cnt = 0
    for i in range(N):
        if bit >> i & 1:
            cnt += 1
    if cnt < K:
        continue

    cost = 0
    maxh = 0
    for i, a in enumerate(A):
        if bit >> i & 1 and maxh >= a:
            cost += maxh - a + 1
            maxh += 1
        elif maxh < a:
            maxh = a


    if cost < ans:
        ans = cost


print(ans)
