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: Wrong Answer)

N,K=list(map(int,input().split()))
height=list(map(int,input().split()))
ans=10**10
count=0
for x in range(1, N):
    if height[0] < height[x]:
        count += 1
if count>=K-1:
    print(0)
    exit()
for i in range(2**N):
    cost=0
    height2=height.copy()
    for j in range(N):
        if i>>j&1:
            count=0
            for k in range(j):
                if height2[k]>=height2[j]:
                    cost+=height2[k]-height2[j]+1
                    height2[j]+=height2[k]-height2[j]+1
            for x in range(1,N):
                if height2[0]<height2[x]:
                    count+=1

            if ans>cost and count==K-1:
                ans=cost


print(ans)