Party Lamps

Description:

To brighten up the gala dinner of the IOI'98 we have a set of N (10 <= N <= 100) colored lamps numbered from 1 to N.
The lamps are connected to four buttons:
Button 1: When this button is pressed, all the lamps change their state: those that are ON are turned OFF and those that are OFF are turned ON.
Button 2: Changes the state of all the odd numbered lamps.
Button 3: Changes the state of all the even numbered lamps.
Button 4: Changes the state of the lamps whose number is of the form 3xK+1 (with K>=0), i.e., 1,4,7,...
A counter C records the total number of button presses.

When the party starts, all the lamps are ON and the counter C is set to zero.

You are given the value of counter C (0 <= C <= 10000) and the final state of some of the lamps after some operations have been executed. Write a program to determine all the possible final configurations of the N lamps that are consistent with the given information, without repetitions.

Input:

Line 1:
 N
 
Line 2:
 Final value of C
 
Line 3:
 Some lamp numbers ON in the final configuration, separated by one space and terminated by the integer -1.
 
Line 4:
 Some lamp numbers OFF in the final configuration, separated by one space and terminated by the integer -1. No lamp will be listed twice in the input.

Output:

Lines with all the possible final configurations (without repetitions) of all the lamps. Each line has N characters, where the first character represents the state of lamp 1 and the last character represents the state of lamp N. A 0 (zero) stands for a lamp that is OFF, and a 1 (one) stands for a lamp that is ON. The lines must be ordered from least to largest (as binary numbers).

If there are no possible configurations, output a single line with the single word `IMPOSSIBLE'

Sample Input:

10
1
-1
7 -1

Sample Output:

0000000000
0101010101
0110110110

Note:

 

本题由旧版NOJ导入，来源：JSOI2010