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 = map(int, input().split())
x = list(map(int,input().split()))
b = [list(map(int,bin(x)[2:].zfill(n))) for x in range(2**n)]
h = [0]*n

for i in range(1,n):
    h[i]=max(h[i-1],x[i-1])

mi = float('inf')
for bit in b:
    ans = 0
    s1=0
    if sum(bit)>=k and bit[0]==1:
        for i in range(n):
            if bit[i]==1:
                s2=x[i]
                if s2<s1:
                    ans+=s1-s2+1
                    s2=s1+1
                if s2<h[i]:
                    ans += h[i]-s2+1
                    s2=h[i]+1
                s1=s2
    if ans!=0:
        mi=min(mi,ans)
print(mi)