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

題意：T組樣例，每組給你n表示n個人，m表示要打m輪比賽。每一輪每個人都要有一個對手。而且每個對手只能打一次。假設a與b打了，c與d打了，那麼下一輪如果a與c打了，那麼b就必須和d打。

問你這m輪比賽怎麼安排。如果無法安排，輸出Impossible。

如果有，m行，每行輸出每個人的對手是幾號。

思路：比賽的時候思維僵化了。

問題轉化為找到m個二階置換{f_i}，使得對於任意i!=j都有f_i(a)!=f_j(a)且f_i(f_j(a))=f_j(f_i(a))。

再想一想異或的性質，你馬上就會做了。
 

#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;
}

抄的大神部落格