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E - Non-triangular Triplets /

Time Limit: 2 sec / Memory Limit: 1024 MB

問題文

• 1 以上 N 以下のすべての整数 i に対して a_i + b_i \leqq c_i が成り立つ。

また、可能な場合はそのような分割を 1 つ構成してください。

• 1 ≦ N ≦ 10^5
• 1 ≦ K ≦ 10^9

入力

N K


出力

a_1 b_1 c_1
:
a_N b_N c_N


入力例 1

1 1


出力例 1

1 2 3


入力例 2

3 3


出力例 2

-1


Score : 700 points

Problem Statement

Given are positive integers N and K.

Determine if the 3N integers K, K+1, ..., K+3N-1 can be partitioned into N triples (a_1,b_1,c_1), ..., (a_N,b_N,c_N) so that the condition below is satisfied. Any of the integers K, K+1, ..., K+3N-1 must appear in exactly one of those triples.

• For every integer i from 1 to N, a_i + b_i \leq c_i holds.

If the answer is yes, construct one such partition.

Constraints

• 1 \leq N \leq 10^5
• 1 \leq K \leq 10^9

Input

Input is given from Standard Input in the following format:

N K


Output

If it is impossible to partition the integers satisfying the condition, print -1. If it is possible, print N triples in the following format:

a_1 b_1 c_1
:
a_N b_N c_N


Sample Input 1

1 1


Sample Output 1

1 2 3


Sample Input 2

3 3


Sample Output 2

-1