Score : $400$ points

Problem Statement

Given a sequence of $N$ positive integers $A=(A_1,A_2,\dots,A_N)$, find every integer $k$ between $1$ and $M$ (inclusive) that satisfies the following condition:

• $\gcd(A_i,k)=1$ for every integer $i$ such that $1 \le i \le N$.

Constraints

• All values in input are integers.
• $1 \le N,M \le 10^5$
• $1 \le A_i \le 10^5$

Input

Input is given from Standard Input in the following format:

$N$ $M$

$A_1$ $A_2$ $\dots$ $A_N$

Output

In the first line, print $x$: the number of integers satisfying the requirement. In the following $x$ lines, print the integers satisfying the requirement, in ascending order, each in its own line.

3 12
6 1 5

3
1
7
11

For example, $7$ has the properties $\gcd(6,7)=1,\gcd(1,7)=1,\gcd(5,7)=1$, so it is included in the set of integers satisfying the requirement. On the other hand, $9$ has the property $\gcd(6,9)=3$, so it is not included in that set. We have three integers between $1$ and $12$ that satisfy the condition: $1$, $7$, and $11$. Be sure to print them in ascending order.