Greatest Common Divisor

Today at the math class the sixth-grader Peter studied the concept of greatest common divisor. Peter immediately decided to apply this knowledge in practice.

Peter wrote on a piece of paper $n$ integers $a_1,a_2,...,a_n$ — the house numbers, where his friends live. Now he wants to choose a subset from these numbers so that their greatest common divisor equals to his favorite number $d$.

Help Peter to choose from given numbers the desired subset.

Input

First line contains two integers $n$ and $d(1\le n\le 1000,1\le d\le 10^9)$. Second line contains $n$ integers $a_1,a_2,...,a_n(1\le a_i\le 10^9)$.

Output

If there is a desired subset, print in the first line number the size $k$ of this subset. On the second line print the numbers included in this subset.

If solution does not exist, print number $-1$.

If there are several answers, print any of them.

Examples