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 sys import stdin
n,k = map(int,stdin.readline().split())
a = map(int,stdin.readline().split())
def solve(b):
    req = 0
    ans = 0
    pr = b[0]-1
    for ii in b:
        i = ii
        if i <= pr:
            ans += pr+1-i
            i = pr+1
        pr = i
    return ans


ma = 1<<n
res = 10**38
for mask in xrange(ma):
    b = [a[0]]
    ma = a[0]
    pr = a[0]
    for i in xrange(1,n):
        if mask & (1<<i):
            b.append(a[i])
        elif a[i] > pr:
            b.append(a[i])
            
        pr = max(pr,a[i])
    if len(b)>=k:
        res = min(res, solve(b[:k]))
print res
            