p02869 NIKKEI Programming Contest 2019-2 - 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
```python
n,k=map(int,input().split())
if 2*k-1>n:
  print(-1)
else:
  a=[i for i in range(k,k+n)]
  A=[]
  for i in range(len(a)):
    if i%2==0:
      A.append(a[i])
  for i in range(len(a)):
    if i%2==1:
      A.append(a[i])
  b1=[i for i in range(k+n,k+n+(n+1)//2)]
  b2=[i for i in range(k+n+(n+1)//2,k+2*n)]
  b1.reverse()
  b2.reverse()
  B=b1+b2
  C=[i for i in range(k+2*n,k+3*n)]
  for i in range(n):
    print(A[i],B[i],C[i])
```