Problem 2893 --2.2.4 Party Lamps

2893: 2.2.4 Party Lamps

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Time Limit $1$ 秒/Second(s) Memory Limit $512$ 兆字节/Megabyte(s)
提交总数 $3$ 正确数量 $1$
裁判形式 标准裁判/Standard Judge 我的状态 尚未尝试
难度 分类标签 usaco 模拟

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.

PROGRAM NAME: lamps

Input

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. 

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). Please print "IMPOSSIBLE" without result.

Sample Input复制

10
1
-1
7 -1

Sample Output复制

0000000000
0101010101
0110110110

提示

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

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.  


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本题记录 用 户（点击查看用户） 运行号（点击购买题解） 时 间
算法最快[$0 $ms] 计爱玲 447784 2019-07-17 08:43:20
内存最少[$2024 $KB] 计爱玲 447784 2019-07-17 08:43:20
第一AC 计爱玲 447784 2019-07-17 08:43:20
第一挑战 计爱玲 447782 2019-07-17 08:33:23

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