Permutation Subsequence

Given two arrays which are permutations, 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, an example of such a sequence. If there are several solutions, you can print any of them.

Constraints

$1 \le n,m \le 2 \cdot 10^5$

$1 \le a_i \le n$

$1 \le b_i \le m$

Example

Input

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

Output

3
1 2 4