## Capitalist Country

Victor lives in a capitalist country where every day, out of the citizens who have money, the top of citizens earn one dollar while everyone else loses one dollar. When a citizen runs out of money, he goes bankrupt and ~~loses his citizenship too~~ is no longer one of the citizens with money. At first, there are citizens and the citizen has dollars. Each citizen has a distinct number of dollars to begin with. Victor would like to know how many days there are until each citizen runs out of money.

#### Input Specification

The first line contains integers , , and (, ), the number of citizens in the country and the special numbers and .

The next line will have a list of integers, (), the of which is how many dollars the citizen has. No two citizens have the same amount of money ( if ). The amount of money of the citizens are **sorted in increasing order.**

#### Output Specification

In one line, print integers, the of which is how many days there are until the citizen runs out of money **modulo **.

#### Sample Input 1

```
5 1 2
1 2 3 4 5
```

#### Sample Output 1

`1 2 3 8 21`

#### Sample Input 2

```
2 1 2
999999999 1000000000
```

#### Sample Output 2

`999999999 999999984`

#### Explanation for Sample 1

At the start, the money count is `1 2 3 4 5`

.

On day 1, the top citizens gain money, and everyone else loses money. Thus, the new money count becomes `0 1 2 5 6`

. Here, citizen 1 goes bankrupt on day 1.

The rest of the days are:

`0 0 1 6 7`

Citizen 2 goes bankrupt on day 2.

`0 0 0 5 8`

Citizen 3 goes bankrupt on day 3.

`0 0 0 4 9`

`0 0 0 3 10`

`0 0 0 2 11`

`0 0 0 1 12`

`0 0 0 0 13`

Citizen 4 goes bankrupt on day 8.

`0 0 0 0 12`

...

`0 0 0 0 1`

`0 0 0 0 0`

The capitalist game finally ends when citizen 5 goes bankrupt on day 21.

## Comments