#include<iostream>
#include<cstdio>
using namespace std;
const int N=205;
int n,k;
int main()
{
	scanf("%d%d",&n,&k);
	if(2*k>n+1)
	{
		printf("-1");
		return 0;
	}
	int l=n/2,r=2*n-1;
	for(int i=3*n-1;i>=2*n;i--)
	{
		printf("%d %d %d\n",l+k,r+k,i+k);
		r-=2;
		if(r<n) r=2*n-2;
		l++;
		if(l==n) l=0;
	}
	return 0;
}
### Prompt

Your task is to create a Cpp solution to 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<iostream>
#include<cstdio>
using namespace std;
const int N=205;
int n,k;
int main()
{
	scanf("%d%d",&n,&k);
	if(2*k>n+1)
	{
		printf("-1");
		return 0;
	}
	int l=n/2,r=2*n-1;
	for(int i=3*n-1;i>=2*n;i--)
	{
		printf("%d %d %d\n",l+k,r+k,i+k);
		r-=2;
		if(r<n) r=2*n-2;
		l++;
		if(l==n) l=0;
	}
	return 0;
}
```