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

stdin = sys.stdin

ni = lambda: int(ns())
na = lambda: list(map(int, stdin.readline().split()))
ns = lambda: stdin.readline().rstrip()  # ignore trailing spaces
nl = lambda: list(map(int, stdin.readline().split()))

n, K = na()
a = na()
ans = float('inf')
for i in range(2**(n-1)):
    colors = 1
    cost = 0
    tmp = a[0]
    for k in range(n-1):
        if tmp < a[k+1]:
            colors += 1
            tmp = a[k+1]
            continue
        if (i >> k) & 1:
            cost += tmp - a[k+1] + 1
            colors += 1
            tmp += 1
    if colors >= K:
        ans = min(ans, cost)
print(ans)
