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

Example Output

3
1 2 4