polski
Task Strong-box (sej)
Strong-box
Memory limit: 32 MB
ByteGuy owns a strong-box protected with a lock.
This lock has 
knobs. Each knob can be
situated in one of 
possible positions.
ByteGuy has not used his strong-box for a long time now, so he has
forgotten the configuration of knobs which opens the strong-box.
He went to the company producing locks, where he learned about
construction of the lock. It consists of 
knobs and the same number of
bolts. All of them (both bolts and knobs) can be
in one of 
allowed positions numbered from 
to 
.
The lock opens, when all of the bolts are set to the position 
.
Turning 
-th knob by one position (from position 
to 
, from 
to 
, 
, from 
to 
,
from 
to 
) causes, that 
-th bolt rotates by 
positions (from position
to 
). The manufacturer of locks helped ByteGuy and gave him a modern 3D-scaner, which allowed to check the configuration of the bolts hidden inside a strong-box.
Locks manufactured for strong-boxes are of high quality and there is only one configuration of knobs which opens the lock.
Task
Write a program, which:
- reads the description of a lock in ByteGuys's strong-box,
- computes the configuration of knobs which opens the lock,
- writes the result to the standard output.
Input
The first line contains two integers 
- the number of knobs,
and the prime number 
- the number of possible positions of knobs, 
.
The following line contains 
integers in the range 
- positions, in which successive knobs are located.
The third line contains 
integers from the range 
- positions of consecutive bolts of ByteGuy's strong-box.
Following 
lines contain descriptions of consecutive knobs -
-th of these lines contains exactly 
integers -
, 
, 
, 
, 
.
Output
The only line of output should contain 
integers from the range 
, separated with
single spaces - the configuration of knobs which opens the lock.
Example
For the input data:
2 3 1 1 2 2 1 0 0 1
the correct result is:
2 2
Task author: Piotr Stanczyk.