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.