Codeforces Round 499 (Div. 1) |
---|

Finished |

Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

number theory

*1800

No tag edit access

The problem statement has recently been changed. View the changes.

×
C. Border

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputAstronaut Natasha arrived on Mars. She knows that the Martians are very poor aliens. To ensure a better life for the Mars citizens, their emperor decided to take tax from every tourist who visited the planet. Natasha is the inhabitant of Earth, therefore she had to pay the tax to enter the territory of Mars.

There are $$$n$$$ banknote denominations on Mars: the value of $$$i$$$-th banknote is $$$a_i$$$. Natasha has an infinite number of banknotes of each denomination.

Martians have $$$k$$$ fingers on their hands, so they use a number system with base $$$k$$$. In addition, the Martians consider the digit $$$d$$$ (in the number system with base $$$k$$$) divine. Thus, if the last digit in Natasha's tax amount written in the number system with the base $$$k$$$ is $$$d$$$, the Martians will be happy. Unfortunately, Natasha does not know the Martians' divine digit yet.

Determine for which values $$$d$$$ Natasha can make the Martians happy.

Natasha can use only her banknotes. Martians don't give her change.

Input

The first line contains two integers $$$n$$$ and $$$k$$$ ($$$1 \le n \le 100\,000$$$, $$$2 \le k \le 100\,000$$$) — the number of denominations of banknotes and the base of the number system on Mars.

The second line contains $$$n$$$ integers $$$a_1, a_2, \ldots, a_n$$$ ($$$1 \le a_i \le 10^9$$$) — denominations of banknotes on Mars.

All numbers are given in decimal notation.

Output

On the first line output the number of values $$$d$$$ for which Natasha can make the Martians happy.

In the second line, output all these values in increasing order.

Print all numbers in decimal notation.

Examples

Input

2 8

12 20

Output

2

0 4

Input

3 10

10 20 30

Output

1

0

Note

Consider the first test case. It uses the octal number system.

If you take one banknote with the value of $$$12$$$, you will get $$$14_8$$$ in octal system. The last digit is $$$4_8$$$.

If you take one banknote with the value of $$$12$$$ and one banknote with the value of $$$20$$$, the total value will be $$$32$$$. In the octal system, it is $$$40_8$$$. The last digit is $$$0_8$$$.

If you take two banknotes with the value of $$$20$$$, the total value will be $$$40$$$, this is $$$50_8$$$ in the octal system. The last digit is $$$0_8$$$.

No other digits other than $$$0_8$$$ and $$$4_8$$$ can be obtained. Digits $$$0_8$$$ and $$$4_8$$$ could also be obtained in other ways.

The second test case uses the decimal number system. The nominals of all banknotes end with zero, so Natasha can give the Martians only the amount whose decimal notation also ends with zero.

Codeforces (c) Copyright 2010-2023 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Sep/25/2023 19:00:35 (l2).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|