#include<cstdio>
#include<algorithm>
#include<cstring>
using namespace std;
int n,k;
int main()
{
	scanf("%d%d",&n,&k);
	if(k>(n+1)/2)
	{
		printf("-1\n");
		return 0;
	}
	int kk=(n+1)/2;
	int a=kk+n*2-1;
	int b=kk+n*3-1-(kk+n*2-1);
	for(int j=kk+n*3-1;j>=kk+n*2-1;j-=2,a--,b--)
	{
		int v=j-kk+k;
		if(j==kk+n*2-1)v++;
		printf("%d %d %d\n",b-kk+k,a-kk+k,v);
	}
	b=kk+n-1;
	for(int j=kk+n*3-2;a>=kk+n;a--,b--,j-=2)
	{
		printf("%d %d %d\n",b-kk+k,a-kk+k,j-kk+k);
	}
	return 0;
}
### Prompt

Your challenge is to write 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<cstdio>
#include<algorithm>
#include<cstring>
using namespace std;
int n,k;
int main()
{
	scanf("%d%d",&n,&k);
	if(k>(n+1)/2)
	{
		printf("-1\n");
		return 0;
	}
	int kk=(n+1)/2;
	int a=kk+n*2-1;
	int b=kk+n*3-1-(kk+n*2-1);
	for(int j=kk+n*3-1;j>=kk+n*2-1;j-=2,a--,b--)
	{
		int v=j-kk+k;
		if(j==kk+n*2-1)v++;
		printf("%d %d %d\n",b-kk+k,a-kk+k,v);
	}
	b=kk+n-1;
	for(int j=kk+n*3-2;a>=kk+n;a--,b--,j-=2)
	{
		printf("%d %d %d\n",b-kk+k,a-kk+k,j-kk+k);
	}
	return 0;
}
```