Little Ivan likes to play **Yamb** and read Marvel superhero comics. His
favorite superhero is spider-man, a friendly neighbourhood teenager named
Peter Parker who got his superpowers via a radioactive spider bite. Ivan
fantasizes that one day he will be able to jump from one skyscraper to
another, just like spider-man does in the comics. During one such fantasy,
he fell asleep.

In his dream he was no longer named Ivan, his name was Peter Parkour and, you guessed it, he was able to use his parkour skills to jump between skyscrapers. He quickly realized that there are exactly skyscrapers in his surroundings and he somehow knew that -th of those skyscrapers is meters tall. He knows that he is able to jump from the -th skyscraper to the -th skyscraper if the remainder when dividing with is equal to . Help Ivan determine, for every skyscraper, the number of other skyscrapers he can jump to.

#### Input

The first line contains two integers and from the task description.

The next line contains integers from the task description.

#### Output

In a single line you should output space-separated integers such that the -th of those integers represents the number of different skyscrapers on which Peter Parkour can jump on if he jumps from the -th skyscraper.

#### Scoring

In test cases worth a total of points, it will hold

In test cases worth an additional points, there will be at most skyscrapers of different heights.

In test cases worth an additional points, it will hold .

#### Sample Input 1

```
2 1
5 5
```

#### Sample Output 1

`0 0`

#### Sample Input 2

```
6 3
4 3 12 6 8 2
```

#### Sample Output 2

`0 4 0 0 0 0`

#### Sample Input 3

```
5 1
1 3 5 7 2
```

#### Sample Output 3

`4 1 1 2 0`

#### Explanation for Sample Output 3

From the first skyscraper of height Peter can jump on any other skyscraper.

From the second skyscraper of height Peter can jump only on a skyscraper of height .

From the third skyscraper of height Peter can jump only on a skyscraper of height .

From the fourth skyscraper of height Peter can jump on skyscrapers of heights and .

From the fifth skyscraper of height Peter cannot jump on any other skyscraper.

## Comments