2 - Non-triangular Triplets

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

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

Examples

Input

1 1

Output

1 2 3

Input

3 3

Output

-1

inputFormat

Input

Input is given from Standard Input in the following format:

N K

outputFormat

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

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

Examples

Input

1 1

Output

1 2 3

Input

3 3

Output

-1

样例

3 3

-1