Contest Duration: - (local time) (200 minutes)
B - Buildings are Colorful! /

Time Limit: 1 sec / Memory Limit: 256 MB

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].

### 問題文

N 個の建物が左から右へと一直線上に並んでいます。左から i 番目の建物は色 i で塗られており、高さは現在 a_i です。 高橋君は市長である。彼はカラフルなものが好きなので、左から見たときに K 色以上の色の建物が見えるという条件を満たしてほしいと思いました。

そのとき、高橋君の目的を達成するために必要な金額を求めなさい。
ただし、「建物 i が見える」とは、建物jの高さ ≥ 建物iの高さ (j < i) となるような j が存在しないのと同じものとします。

### 入力

N K
a_1 a_2 a_3 ... a_N


また、最後には改行を入れること。

### 制約

• 1 ≤ K ≤ N ≤ 15
• 1 ≤ a_i ≤ 10^9

• N = K

• N ≤ 5
• a_i ≤ 7

• 追加の制約はない。

### 入力例1

5 5
3949 3774 3598 3469 3424


### 出力例1

1541


### 入力例2

5 3
7 4 2 6 4


### 出力例2

7