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.

Sample Input 1

3 12
6 1 5

Sample Output 1

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.