Buildings are Colorful!

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.

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.

Input Format

N K a_1 a_2 a_3 ... a_N

Example

Input

5 5 3949 3774 3598 3469 3424

Output

1541

inputFormat

Input Format

N K a_1 a_2 a_3 ... a_N

outputFormat

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.

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.

Input Format

N K a_1 a_2 a_3 ... a_N

Example

Input

5 5 3949 3774 3598 3469 3424

Output

1541

样例

5 5
3949 3774 3598 3469 3424

1541