Easy Equation

문제

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:

a² + b² + c² = k (ab + bc + ca) + 1.

Given positive integers n and k, find n arbitrary triples (a₁, b₁, c₁), (a₂, b₂, c₂), . . . , (a_n, b_n, c_n) that all satisfy the equation. Furthermore, all 3n integers a₁, . . . , a_n, b₁, . . . , b_n, c₁, . . . , c_n should be different positive integers with at most 100 decimal digits each.

입력

The first line contains two integers k and n (2 ≤ k ≤ 1 000, 1 ≤ n ≤ 1 000) — the constant k in the equation and the target number of triples.

출력

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.

2 8

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

3 3

1 3 12
8 21 87
44 165 615