Problem:
Max Score: 350 Points

Problem Statement

There are N buildings along the line. The i-th building from the left is colored in color i, and its height is currently a_i meters.

Chokudai is a mayor of the city, and he loves colorful thigs. And now he wants to see at least K buildings from the left.

You can increase height of buildings, but it costs 1 yens to increase 1 meters. It means you cannot make building that height is not integer.

You cannot decrease height of buildings.

Calculate the minimum cost of satisfying Chokudai's objective.

Note: "Building i can see from the left" means there are no j exists that (height of building j) ≥ (height of building i) and j < i.

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.

Sample Input 1

5 5
3949 3774 3598 3469 3424

Sample Output 1

1541

The optimal solution is (height of buildings from the left) = [3949, 3950, 3951, 3952, 3953].

Sample Input 2

5 3
7 4 2 6 4

Sample Output 2

7

The optimal solution is (height of buildings from the left) = [7, 8, 2, 9, 4].

Solution in Python (3.4.3) (judge verdict: Accepted)

import itertools

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

amin=10**9*20
for i in itertools.product([0,1], repeat=n):
    if sum(i)==k:
        hs=a[0]
        acnt=0
        h=[]
        for j in range(n):
            if i[j]==1 and j>0:
                if hs>=a[j]:
                    acnt+=hs-a[j]+1
                    hs=hs+1
            if hs<a[j]:
                hs=a[j]
            h.append(hs)
#        print(i,acnt,h)
        amin=min(amin,acnt)
        
print(amin)