#include <cstdio>

int main()
{
  int n,k;
  scanf("%d%d",&n,&k);
  if(k<=(n+1)/2){
    int s=(n+1)/2;
    for(int i=0;i<s;i++){
      printf("%d %d %d\n",k+i,k+2*n-s+i,k+2*n+2*i);
    }
    for(int i=0;i<n-s;i++){
      printf("%d %d %d\n",k+s+i,k+n+i,k+2*n+2*i+1);
    }
  }
  else{
    puts("-1");
  }
  return 0;
}

### Prompt

In CPP, your task is to solve the following problem:

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

### Response

```cpp
#include <cstdio>

int main()
{
  int n,k;
  scanf("%d%d",&n,&k);
  if(k<=(n+1)/2){
    int s=(n+1)/2;
    for(int i=0;i<s;i++){
      printf("%d %d %d\n",k+i,k+2*n-s+i,k+2*n+2*i);
    }
    for(int i=0;i<n-s;i++){
      printf("%d %d %d\n",k+s+i,k+n+i,k+2*n+2*i+1);
    }
  }
  else{
    puts("-1");
  }
  return 0;
}

```