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: Accepted)

# Square869120Contest #4 B - Buildings are Colorful!　
# 全探探索　ver

import sys

N, K = map(int, sys.stdin.readline().strip().split())
a = list(map(int, sys.stdin.readline().strip().split()))

ans = float('inf')
for i in range(2 ** (N - 1)):
    bit = [(i >> j) & 1 for j in range(N - 1)]  # 左から2番目以降で見えるようにするビルを選択

    can_see = 0
    cost = 0
    height = a[0]
    for j, b in enumerate(bit):
        if (b == 1) & (height >= a[j + 1]):
            cost += height - a[j + 1] + 1
            height = height + 1
            can_see += 1
        elif (b == 1):
            height = a[j + 1]
            can_see += 1
        elif height < a[j + 1]:
            can_see += 1
            height = a[j + 1]

    if can_see >= K - 1:
        ans = min(ans, cost)

print(ans)