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Astronaut 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.

宇航员娜塔莎抵达了火星。她知道火星人是非常贫穷的外星人。为了改善火星公民的生活，他们的皇帝决定向每一位访问该星球的游客征税。娜塔莎是地球居民，因此她必须缴纳税款才能进入火星领土。

火星上有 $n$ 种纸币面额：第 $i$ 种纸币的面值为 $a_i$。娜塔莎拥有每种面额的无限张纸币。

火星人每只手有 $k$ 根手指，因此他们使用以 $k$ 为底的进位制。此外，火星人认为数字 $d$（在以 $k$ 为底的进位制中）是“神圣的”。因此，若娜塔莎所缴税款金额用 $k$ 进制表示时，其末位数字恰好为 $d$，火星人便会感到高兴。不幸的是，娜塔莎目前尚不知道火星人的神圣数字 $d$ 是多少。

请确定：对于哪些 $d$ 值，娜塔莎能够使火星人感到高兴？

娜塔莎只能使用她自己所拥有的纸币。火星人不会给她找零。

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.

第一行包含两个整数 $n$ 和 $k$（$1 \le n \le 100\,000$，$2 \le k \le 100\,000$）—— 分别表示火星上纸币的面额种类数以及火星所用数制的进制。

第二行包含 $n$ 个整数 $a_1, a_2, \ldots, a_n$（$1 \le a_i \le 10^9$）—— 表示火星上纸币的各个面额。

所有数字均以十进制给出。

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.

第一行输出 Natasha 能够使火星人开心的数值 $d$ 的个数。

第二行按升序输出所有这些数值。

所有数字均以十进制表示。

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.

考虑第一个测试用例，它使用八进制数制。

若取一张面值为 $12$ 的纸币，则总金额为 $12$，在八进制下表示为 $14_8$，其末位数字为 $4_8$。

若取一张面值为 $12$ 的纸币和一张面值为 $20$ 的纸币，则总金额为 $32$，在八进制下表示为 $40_8$，其末位数字为 $0_8$。

若取两张面值为 $20$ 的纸币，则总金额为 $40$，在八进制下表示为 $50_8$，其末位数字为 $0_8$。

除 $0_8$ 和 $4_8$ 外，无法得到其他末位数字。而 $0_8$ 和 $4_8$ 还可通过其他方式得到。

第二个测试用例使用十进制数制。所有纸币的面额均以 $0$ 结尾，因此娜塔莎只能向火星人支付一个其十进制表示也以 $0$ 结尾的金额。