D. Dangerous Data
time limit per test
2 seconds
memory limit per test
1024 megabytes
input
standard input
output
standard output

Mr. Nežmah has started working as a secret agent for SOA. Evil Mr. M has a secret set of $$$n + k$$$ distinct integers, and SOA has already figured out $$$n$$$ of them. Nežmah is currently in Mr. M's secret lair and has access to all of the $$$n + k$$$ integers. However, he can only memorize $$$k$$$ integers, and he doesn't know which $$$n$$$ integers SOA already knows. Help Nežmah construct $$$k$$$ integers (not necessarily from Mr. M's set) to remember so that he can figure out what integers SOA is missing once he comes back.

This is a run twice problem.

In the first run, you are given $$$n$$$ and $$$k$$$, and $$$n + k$$$ different integers. You have to output $$$k$$$ integers.

In the second run, you are given $$$n$$$ and $$$k$$$ and $$$n$$$ integers which form a proper subset of the $$$n + k$$$ integers given in the first run. The order may be shuffled. You are also given the $$$k$$$ integers outputted in the first run in the same order. You should output the missing $$$k$$$ integers from the first input.

Input

In the first run:

The first line contains the word first and the numbers $$$n$$$ and $$$k$$$ ($$$1 \leq n \leq 10^5$$$, $$$1 \leq k \leq 10$$$).

The second line contains $$$n+k$$$ integers $$$a_i$$$, the elements of Mr. M's set $$$(1 \leq a_i \leq 10^6)$$$.

In the second run:

The first line contains the word second and the numbers $$$n$$$ and $$$k$$$.

The second line contains $$$k$$$ integers, the output of your first run.

The third line contains $$$n$$$ integers $$$b_i$$$, the elements of Mr. M's set that SOA has already figured out ($$$1 \leq b_i \leq 10^6$$$).

Output

In the first run, output a single line with $$$k$$$ integers $$$m_i$$$ $$$(0 \leq m_i \lt 2^{20})$$$.

In the second run, output a single line with the $$$k$$$ required elements in any order.

Examples
Input
first 3 2
5 2 3 4 1
Output


12345 0
Input
second 3 2
12345 0
3 1 5
Output



4 2