Magic of David Copperfield

The well-known magician David Copperfield loves to show the following trick: a square with N rows and Ncolumns of different pictures appears on a TV screen. Let us number all the pictures in the
following order:

1	2		N
N*(N-1)+1	N*(N-1)+2		N*N

Each member of the audience is asked to put a finger on the upper left picture (i.e., picture number one) and The Magic begins: the magician tells the audience to move the finger k₁ times through
the pictures (each move is a shift of the finger to the adjacent picture up, down, left or right provided that there is a picture to move to), then with a slight movement of his hand he removes some of the pictures with an exclamation ``You are not there!",
and ... it is true - your finger is not pointing to any of the pictures removed. Then again, he tells the audience to make k<sub>2</sub> moves, and so on. At the end he removes all the pictures but one and smiling triumphantly declares, ``I've
caught you" (applause).

Just now, David is trying to repeat this trick. Unfortunately, he had a hard day before, and you know how hard to conjure with a headache. You have to write a program that will help David to make his trick.

Input 

The input begins with a single positive integer on a line by itself indicating the number of the cases following, each of them as described below. This line is followed by a blank line, and there is also
a blank line between two consecutive inputs.

Each test case consists of a single integer number N ( ).

Output 

For each test case, the output must follow the description below. The outputs of two consecutive cases will be separated by a blank line.

Your program should write the following lines with numbers to the output file:

where k_i is a number of moves the audience should make on the i-th turn ( ). All k_i should
be different (i.e. k_i <> k_j when i <> j).  are
the numbers of the pictures David should remove after the audience will make k_i moves (the number of the pictures removed is arbitrary, but each picture should be listed only once, and at least one picture should be removed on
each turn).

A description of the every next turn should begin with a new line. All numbers on each line should be separated by one or more spaces. After e iterations, all pictures except one should be removed.

Sample input 

1

3

Sample Output 

8     4 6
13    9
10    7 1
7     8
11    3 5

题意：大卫科波菲尔表演魔术，让一个个观众上台，手指从第一张卡片开始移动一个步数，然后大卫删除掉一些观众不可能最终指到的卡片，直到最后删除到剩1张。

思路：想通了其实很简单的构造问题，以斜对角线为行号，如果走的奇数步，那么必然不会停留在当前行号，这样每次走奇数步，然后把当前一行消掉，最终走到右下角就是答案。

代码：

#include <stdio.h>
#include <string.h>

int t, n, k, m;

void init() {
	scanf("%d", &n);
	k = 2 * n + 1;
	m = 2;
}

void solve() {
	while (k && m < 2 * n) {
		printf("%d", k);
		for (int i = 1; i < m; i++) {
			if (i > n || m - i > n) continue;
			printf(" %d", (i - 1) * n + (m - i));
		}
		printf("\n");
		m++; k += 2;
	}
	if (t) printf("\n");
}

int main() {
	scanf("%d", &t);
	while (t--) {
		init();
		solve();
	}
	return 0;
}