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 (3.8.2) (judge verdict: Wrong Answer)

#
# s8pc4 b
#
import sys
from io import StringIO
import unittest


class TestClass(unittest.TestCase):
    def assertIO(self, input, output):
        stdout, stdin = sys.stdout, sys.stdin
        sys.stdout, sys.stdin = StringIO(), StringIO(input)
        resolve()
        sys.stdout.seek(0)
        out = sys.stdout.read()[:-1]
        sys.stdout, sys.stdin = stdout, stdin
        self.assertEqual(out, output)

    def test_入力例1(self):
        input = """5 5
3949 3774 3598 3469 3424"""
        output = """1541"""
        self.assertIO(input, output)

    def test_入力例2(self):
        input = """5 3
7 4 2 6 4"""
        output = """7"""
        self.assertIO(input, output)


def resolve():
    N, K = map(int, input().split())
    a0, *A = map(int, input().split())

    ans = float("inf")
    for bit in range(1 << (N-1)):
        if bin(bit).count("1") != K-1:
            continue
        tmp = 0
        n = 1
        for i, a in enumerate(A):
            if (1 << i) & bit == (1 << i):
                tmp += max(0, a0-a+n)
                n += 1
        ans = min(ans, tmp)

    print(ans)


if __name__ == "__main__":
    # unittest.main()
    resolve()