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
import copy
input = sys.stdin.readline

n, k = map(int,input().split())
a = list(map(int,input().split()))

min_c = 10**11

for i in range(2**n):
    c = 0
    r_a = copy.copy(a)
    bit = 2
    max_a = r_a[0]
    for j in range(1,n):
        if i & bit and r_a[j] <= max_a:
            c += max_a - r_a[j] + 1
            r_a[j] = max_a + 1
        if r_a[j] > max_a:
            max_a = r_a[j]
        bit *= 2
    cl = 1
    max_a = r_a[0]
    for j in range(1,n):
        if r_a[j] > max_a:
            cl += 1
            max_a = r_a[j]
    if cl >= k:
        min_c = min(min_c,c)

print (min_c)