DreamGrid, the king of Gridland, is making a knight tournament. There are knights, numbered from 1 to , participating in the tournament. The rules of the tournament are listed as follows:
The tournament consists of rounds. Each round consists of several duels. Each duel happens between exactly two knights.
Each knight must participate in exactly one duel during each round.
For each pair of knights, there can be at most one duel between them during all the rounds.
Let , , and , be four distinct integers. If
Knight fights against knight during round , and
Knight fights against knight during round , and
Knight fights against knight during round ,
then knight must fight against knight during round .
As DreamGrid's general, you are asked to write a program to arrange all the duels in all the rounds, so that the resulting arrangement satisfies the rules above.
Input
There are multiple test cases. The first line of the input is an integer , indicating the number of test cases. For each test case:
The first and only line contains two integers and (), indicating the number of knights participating in the tournament and the number of rounds.
It's guaranteed that neither the sum of nor the sum of in all test cases will exceed 5000.
Output
For each test case:
If it's possible to make a valid arrangement, output lines. On the -th line, output integers separated by one space, indicating that in the -th round, knight will fight against knight for all .
If there are multiple valid answers, output the lexicographically smallest answer.
Consider two answers and , let's denote as the -th integer on the -th line in answer , and as the -th integer on the -th line in answer . Answer is lexicographically smaller than answer , if there exists two integers () and (), such that
for all and , , and
for all , , and finally .
If it's impossible to make a valid arrangement, output "Impossible" (without quotes) in one line.
Please, DO NOT output extra spaces at the end of each line, or your answer may be considered incorrect!
Sample Input
2
3 1
4 3
Sample Output
Impossible
2 1 4 3
3 4 1 2
4 3 2 1
题意：T组样例，每组给你n表示n个人，m表示要打m轮比赛。每一轮每个人都要有一个对手。而且每个对手只能打一次。假设a与b打了，c与d打了，那么下一轮如果a与c打了，那么b就必须和d打。
问你这m轮比赛怎么安排。如果无法安排，输出Impossible。
如果有，m行，每行输出每个人的对手是几号。
思路：比赛的时候思维僵化了。
问题转化为找到m个二阶置换{f_i}，使得对于任意i!=j都有f_i(a)!=f_j(a)且f_i(f_j(a))=f_j(f_i(a))。
再想一想异或的性质，你马上就会做了。
#include<bits/stdc++.h>
#define ll long long
#define maxn 200010
using namespace std;
int n,m,k;
int main()
{
int T,cas=1;
scanf("%d",&T);
while(T--)
{
scanf("%d%d",&n,&m);
if(m>=(n&(-n))) {puts("Impossible");continue;}
for(int j=1;j<=m;j++)
for(int i=0;i<n;i++)
{
printf("%d%c",(i^j)+1,i==n-1?'\n':' ');
}
}
return 0;
}
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