There is a line of boxes on a table, indexed from to . Each box is assigned a number between and such that every number from to appears at least once. In order to open a box with , you must have already opened a box with . You do not need to open anything before opening a box with .

In addition, to get from index to index , you need to travel a distance of . You are initially at index , and all the boxes are closed. What is the minimum distance you need to travel in order to open a box with ?

#### Constraints

For all subtasks:

- There is always at least one box with for all .

Points Awarded | |
---|---|

5 points | |

10 points |

#### Input Specification

The first line contains two integers and .

The second line contains integers .

#### Output Specification

Output the minimum distance required. Please note that this number may not fit inside a 32-bit integer.

#### Sample Input

```
4 3
3 1 2 2
```

#### Sample Output

`5`

#### Explanation for Sample Output

Starting from index , we go to index , then to index and then back to index . The total distance travelled is . It can be proven that this is the minimal distance required.

## Comments