to (inclusive) are set in a pool of lava. As can be expected, the stones are very hot. In fact, they can be hotter than the surface of the sun! must jump from the start () to the other side (), but he can only jump at most stones forward at a time. Fortunately, has a pair of cooling boots that can cool any stone to degrees. However, the boots require one unit of power per degree cooled, and power is very expensive! Can you help find the minimum units of power required to jump to the other side of the lava pool?

developed a new hopscotch. In this game, a row of stones conveniently numbereddegrees.

can only walk on stones that are() from stone .

can only hop forwards to stoneSince , he can hop to () on his first hop.

starts from#### Input Specification

The first line will contain and , separated by a space.

The second line will contain all () separated by spaces.

There is a trailing newline (ASCII code 10) at the end of input.

#### Output Specification

Output the minimum power cost to hop from to () on the first line.

Output the indices of the stones

must hop on to use the minimum amount of power on the second line, separated by spaces and in ascending order.If there are multiple ways to achieve the minimum power, output the lexicographically most sequence of the indices.

#### Constraints

For all subtasks:

##### Subtask 1 [1/15]

##### Subtask 2 [1/15]

##### Subtask 3 [3/15]

##### Subtask 4 [10/15]

No additional constraints.

#### Sample Input 1

```
16 4
4 5 3 12 2 6 3 6 5 5 16 1 10 9 13 12
```

#### Sample Output 1

```
20
3 5 9 12 14
```

#### Sample Input 2

```
16 2
4 13 6 6 4 1 7 1 0 15 3 0 8 11 5 8
```

#### Sample Output 2

```
32
1 3 5 6 8 9 11 12 13 15
```

## Comments

I keep TLE on case #7 of final batch, how can I optimise my code

I am using monoqueue + a queue that keeps track of indexes of values in the monoqueue. It is an O(N) solution

For some mysterious reason, putting all of my code inside a

`solve()`

function significantly increased the speed of my solution. I would recommend that you, and others who are having trouble passing this question in python, try the same.Edit: I should note that I saw this speedup only when using cpython, not pypy.

Thank you! My code was indeed sped up, but case 7 still does not pass.

What does lexicographically most sequence mean?

Edit: e.g. for the first sample, wouldn't 3 7 10 14 be bigger lexicographically?

3 7 10 14 would be bigger lexicographically but the total cost would be 3 + 3 + 5 + 10 which is 21 so it isn't the minimum cost

Why is this downvoted? Assuming "lexicographically most sequence" means "lexicographically largest sequence" the point holds.

My solution that uses a monoqueue and a hashmap TLEs and occasionally RTEs (WA aside), why is this solution suboptimal? Can someone give me a hint on how to optimize this?

No hashmap is needed.