Coprime

Problem Description

You are given a sequence $A = (A_1, A_2, \dots, A_n)$ of $n$ positive integers. Find every $k$ in $[1, m]$ that satisfies the following condition:

$$\gcd(A_i, k) = 1 \quad \text{for all } 1 \leq i \leq n$$

Input Format

The first line contains two integers $n$ and $m$.

The second line contains $n$ integers giving the sequence $A$.

Output Format

The first line outputs the number of valid $k$'s. Then each following line outputs one valid $k$.

Sample Input

3 12
6 1 5

Sample Output

3
1
7
11

Constraints

$1 \leq n, m \leq 100000$

$1 \leq a_i \leq 100000$