Problem Description

Given an integer \( k \) greater than 1, it is possible to prove that there are infinitely many triples of positive integers \( (a, b, c) \) that satisfy the following equation:

\[ a^2 + b^2 + c^2 = k(ab + bc + ca) + 1 \]

Given positive integers \( n \) and \( k \), find \( n \) arbitrary triples \( (a_1, b_1, c_1), (a_2, b_2, c_2), \cdots , (a_n, b_n, c_n) \) that all satisfy the equation. Furthermore, all \( 3n \) integers \( (a_1, b_1, c_1), (a_2, b_2, c_2), \cdots , (a_n, b_n, c_n) \) should be different positive integers with at most 100 decimal digits each.

Input Format

The first line contains two integers \( k \) and \( n \) \( (2 \leq k \leq 1000, 1 \leq n \leq 1000) \) — the constant \( k \) in the equation and the target number of triples.

Output Format

Output \( n \) lines. The \( i \)-th line should contain three space-separated integers \( a_i \), \( b_i \), and \( c_i \) with at most 100 digits each — the \( i \)-th of the solutions you found.

Sample Input and Output

Sample Input #1

2 8

Sample Output #1

1 2 6
3 10 24
12 35 88
15 28 84
4 5 18
14 33 90
40 104 273
21 60 152

Sample Input #2

3 3

Sample Output #2

1 3 12
8 21 87
44 165 615

见题面 Input 部分

见题面 Output 部分