2.2.4 Party Lamps

Party Lamps
IOI 98

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.

PROGRAM NAME: lamps

INPUT FORMAT

No lamp will be listed twice in the 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.

SAMPLE INPUT (file lamps.in)

10
1
-1
7 -1

In this case, there are 10 lamps and only one button has been pressed. Lamp 7 is OFF in the final configuration.

OUTPUT FORMAT

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 OUTPUT (file lamps.out)

0000000000
0101010101
0110110110

In this case, there are three possible final configurations:

• All lamps are OFF
• Lamps 1, 4, 7, 10 are OFF and lamps 2, 3, 5, 6, 8, 9 are ON.
• Lamps 1, 3, 5, 7, 9 are OFF and lamps 2, 4, 6, 8, 10 are ON.

• {
  ID: makeeca1
  PROG: lamps
  LANG: PASCAL
  }
  program lamps;
  const ds:array[1..8]of byte=(0,56,21,45,18,42,7,63);//²Ù×÷Êý
        dc:array[1..8]of byte=(1,2,1,1,2,1,2,0); //ËùÐè°ŽŒüÊý
  var s1,s2,n,c,i,j:longint; flag:boolean;
  procedure get(var x:longint);
  var t:longint;
  begin
    read(t);
    while t<>-1 do begin
      x:=x or (1<< (t mod 6));//ÌíŒÓ׎̬
      read(t);
    end;
  end;
  begin
    assign(input,'lamps.in');reset(input);
    assign(output,'lamps.out');rewrite(output);
    readln(n);readln(c);get(s1);get(s2);flag:=true;
    if (s1 and s2=0 )then
      for i:=1 to 8 do
      if (dc[i]<=c)and(ds[i] or s1=ds[i]){ds[]°üº¬s1}and(ds[i]and s2=0){ds[]²»°üº¬s2}then begin
        for j:=1 to n do write((ds[i]>> (j mod 6)) and 1);//žô6λѭ»·
        writeln;
        flag:=false;
      end;
    if flag then writeln('IMPOSSIBLE');
    close(input);close(output);
  end.