Given two arrays of integers, find their longest common subsequence.

A subsequence is a sequence of array elements from left to right that can contain gaps. A common subsequence is a subsequence that appears in both arrays.

Input

The first line has two integers $n$ and $m$: the sizes of the arrays.

The second line has $n$ integers $a_1,a_2,\dots,a_n$: the contents of the first array.

The third line has $m$ integers $b_1,b_2,\dots,b_m$: the contents of the second array.

Output

First print the length of the longest common subsequence.

After that, print an example of such a sequence. If there are several solutions, you can print any of them.

Constraints

• $1 \le n,m \le 1000$
• $1 \le a_i, b_i \le 10^9$

Example

Input:

8 6
3 1 3 2 7 4 8 2
6 5 1 2 3 4

Output:

3
1 2 4