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 (3.8.2) (judge verdict: Wrong Answer)

n,k=map(int,input().split())
a=list(map(int,input().split()))
if n==k:
    suma=sum(a)
    m=a[0]+1
    for i in range(1,n):
        x=a[i]
        if x>=m:
            m=x+1
        else:
            a[i]=m
            m+=1
    print(sum(a)-suma)
    exit()
ans=15*10**10
for i in range(2**(n-1)):#1番目は確定だから
    cnt,s,mh=0,0,a[0]+1
    for j in range(n-1):
        if i>>j&1:
            cnt+=1
            x=a[j+1]
            if x>=mh:
                mh=x+1
            else:
                s+=mh-x
                mh+=1
    if cnt>=k-1:
        ans=min(ans,s)
print(ans)