Reference: AtCoder ABC215 D — Coprime 2

You are given a sequence of ~N~ positive integers:

~A_1, A_2, \ldots, A_N~

Find every integer ~k~ between ~1~ and ~M~, inclusive, such that:

~gcd(A_i, k) = 1~

for every ~i~ from ~1~ to ~N~.

Input

• The first line contains two integers ~N~ and ~M~.
• The second line contains ~N~ integers: ~A_1, A_2, \ldots, A_N~.

Output

• First, print the number ~x~ of integers satisfying the condition.
• Then print these ~x~ integers in increasing order, one integer per line.

Constraints

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

Example 1

Input:

3 12
6 1 5

Output:

3
1
7
11