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]
Subtask 2 [90 points]
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].