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 sys

N, K = map(int, sys.stdin.readline().split(" "))
a = list(map(int, sys.stdin.readline().split(" ")))

ans = float("inf")
for i in range(2**N):
    pattern = []
    for j in range(N):
        pattern.append(i >> j & 1)
    if sum(pattern) < K:
        continue
    # print(pattern)

    max_h = 0
    tmp_ans = 0
    for n in range(N):
        if pattern[n] == 1:
            if a[n] <= max_h:
                tmp_ans += max_h - a[n] + 1
                max_h += 1
        max_h = max(max_h, a[n])
    ans = min(ans, tmp_ans)
    
print(ans)