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

cost = 10 ** 9 * n + 1
for i in range(1, 2 ** (n - 1)):
    num = 0
    c = 0
    prev = a[0]
    for j in range(n - 1):
        if num == k - 1:
            break
        if (i >> j & 1) and a[j + 1] <= prev:
            c += prev - a[j + 1] + 1
            prev = prev + 1
            num += 1
        elif (i >> j & 1) and a[j + 1] > prev:
            prev = a[j + 1]
            num += 1
    if num == k - 1:
        cost = min(c, cost)
print(cost)