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

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

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