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

#### Input Specification

The first line contains integers , , and (, ), the number of monkeys 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 monkey has. No two monkeys have the same amount of money ( if ). The amount of money of the monkeys are **sorted in increasing order**.

#### Output Specification

In one line, print integers, the of which is how many days there are until the monkey 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 monkeys gain money, and everyone else loses money. Thus, the new money count becomes `0 1 2 5 6`

. Here, monkey 1 goes bankrupt on day 1.

The rest of the days are:

`0 0 1 6 7`

monkey 2 goes bankrupt on day 2.

`0 0 0 5 8`

monkey 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`

monkey 4 goes bankrupt on day 8.

`0 0 0 0 12`

…

`0 0 0 0 1`

`0 0 0 0 0`

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

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