Score: $800$ points

问题陈述

将边长为 $N$ 的立方体分割成 $N^3$ 个更小的立方体，每个小立方体的边长为 $1$，并从中选择 $K$ 个这样的小立方体。构建一种选择方式，使得从立方体的三个面垂直方向观察时，所有 $K$ 个被选中的小立方体都是可见的，并且呈现出相同的形状。

为了精确地表述问题，我们将分割后每个小立方体与一个整数三元组 $(x_i, y_i, z_i)$ 相关联。

构建并打印一组 $K$ 个整数三元组 $(x_i, y_i, z_i)$，满足以下条件：

• $0 \leq x_i, y_i, z_i < N$
• $\left\lbrace (x_i, y_i) \, \middle| \, 1 \le i \le K \right\rbrace = \left\lbrace (y_i, z_i) \, \middle| \, 1 \le i \le K \right\rbrace = \left\lbrace (z_i, x_i) \, \middle| \, 1 \le i \le K \right\rbrace$
• 上述集合中包含 $K$ 个元素。也就是说，对于 $i \neq j$，$(x_i, y_i) \neq (x_j, y_j)$。

可以证明，对于满足约束条件的任何输入，都存在一个解决方案。

以上为大语言模型 kimi 翻译，仅供参考。

Problem Statement

Divide a cube with a side length of $N$ into $N^3$ smaller cubes, each with a side length of $1$, and select $K$ of these smaller cubes. Construct one way to select them so that, when viewed from any of the three directions perpendicular to the faces of the cubes, all $K$ selected cubes are visible and appear in the same shape.

To formulate the problem precisely, we associate each smaller cube after division with a triple of integers $(x_i, y_i, z_i)$.

Construct and print one set of $K$ triples of integers $(x_i, y_i, z_i)$ that satisfy the following conditions.

• $0 \leq x_i, y_i, z_i < N$
• $\left\lbrace (x_i, y_i) \, \middle| \, 1 \le i \le K \right\rbrace = \left\lbrace (y_i, z_i) \, \middle| \, 1 \le i \le K \right\rbrace = \left\lbrace (z_i, x_i) \, \middle| \, 1 \le i \le K \right\rbrace$
• The set mentioned in the previous item has $K$ elements. That is, $(x_i, y_i) \neq (x_j, y_j)$ for $i \neq j$.

It can be shown that a solution exists for any input satisfying the constraints.

Constraints

• All input values are integers.
• $1 \leq N \leq 500$
• $1 \leq K \leq N^2$

Input

The input is given from Standard Input in the following format:

$N$ $K$

Output

Print your answer in the following format:

$x_1$ $y_1$ $z_1$

$x_2$ $y_2$ $z_2$

$\vdots$

$x_K$ $y_K$ $z_K$

If multiple solutions exist, any of them will be accepted.

Sample Input 1

3 3

Sample Output 1

0 0 0
1 1 1
2 2 2

Sample Input 2

2 4

Sample Output 2

0 0 1
0 1 0
1 0 0
1 1 1

Sample Input 3

1 1

Sample Output 3

0 0 0