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.

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.

Constraints

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

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

见题面 Input 部分

见题面 Output 部分