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
from itertools import combinations
import sys
#input = sys.stdin.buffer.readline
N, K = map(int, input().split())
A = list(map(int, input().split()))
Com = []
for i in range(N):
    Com.append(i)


ans = float('inf')
for com in combinations(Com, K):
    anscom = 0
    thread = 0
    for i, a in enumerate(A):
        if i not in com:
            thread = max(thread, a)
        else:
            if thread < a:
                thread = a
            else:
                anscom += thread + 1 - a
                thread += 1
    ans = min(ans, anscom)
print(ans)


