You are given two sequences of numbers named $A$ and $B$. Your task is to find the longest common increasing subsequence.

In other words, let us assume that $A$ has the length of $n$ and can be shown as $A_1, A_2, ..., A_n$. Also, $B$ has the length of $m$ and can be shown as $B_1, B_2, ..., B_m$.

You are required to find a number $l$ and two sequences of indices named $C$ and $D$ of length $l$ such that the following conditions hold:

• $1 \le C_1 < C_2 < ... < C_l \le n$
• $1 \le D_1 < D_2 < ... < D_l \le m$
• For each $1 \le i \le l$, you are given $A_{C_{i}} = B_{D_{i}}$ (common subsequence condition)
• $A_{C_1} \le A_{C_2} \le ... \le A_{C_l}$ (increasing subsequence condition)
• $B_{D_1} \le B_{D_2} \le ... \le B_{D_l}$ (increasing subsequence condition)

Input format

• The first line contains two integers $n$ and $m$ respectively where $n$ is the length of sequence $A$ and $m$ is the length for $B$.
• The second line contains $n$ space-separated integers that represent the elements of the sequence $A$.
• The third line contains $m$ space-separated integers that represent the elements of the sequence $B$.

Output format

The output contains three lines:

In the first line, print an integer $l$ that denotes the length of the longest common increasing subsequence.

In the second line, print $l$ integers that represent elements of $C$ (chosen indices of subsequence from $A$).

In the third line, print $l$ integers that represent elements of $D$ (chosen indices of subsequence from $B$).

Note

• The elements of $C$ and $D$ must be in increasing order.
• The answer to the problem could be $0$, in this case, you just need to print $0$ in a single line.

Constraints

$1 \le n, m \le 10^{5}$

$1 \le A_i, B_i \le 10^{9}$