Given a sequence of $n$ elements, denoted as $A$. Your task is to transform it into a beautiful sequence of order $d$ by performing the following steps: At each step, choose an element in the sequence and either increase or decrease that element by one unit. The sequence $b_1, b_2, ..., b_n$ is called a beautiful sequence of order $d$ if $b_i = b_{i-1} + d$ for every $i=2,3,...,n$. Find the minimum number of steps to transform $A$ into a beautiful sequence of order $d$.
### Input
- The first line contains two positive integers $n, d (1 \le n \le 1000, 1 \le d \le 10^9)$.
- The second line contains $n$ positive integers $A_i$.
### Output
- Print the minimum number of steps to transform $A$ into a beautiful sequence of order $d$.
### Constraints
- 25% of the tests have $d = 0$ and $|A_i| \le 10^3$.
- 25% of the tests have $d = 0$ and $|A_i| \le 10^9$.
- 25% of the tests have $d = 1$ and $|A_i| \le 10^3$.
- 25% of the tests have $d \le 10^9$ and $|A_i| \le 10^9$.
### Example
Input:
```
3 1
3 2 2
```
Output:
```
3
```
