#include <iostream>
using namespace std;
typedef long long ll;
int main()
{
	ll a,b;
	cin>>b>>a;
	ll r0=a+b*2-1;
	ll s1=(a+r0)*b;
	ll s2=(r0+1+r0+b)*b/2;
	//cout<<s1<<' '<<s2<<endl;
	ll ans;
	if (s1>s2) {
		cout<<-1<<endl;
		return 0;
	}
	else
	{
		ll u=a+1,v;
		if (b%2==1)
		   v=r0-b/2-1;
		else v=r0-b/2;
		for (ll i=r0+1;i<=r0+b;i++)
		{
			cout<<u<<' '<<v--<<' ';
			cout<<i<<endl;
			u+=2;
			if (u>=a+b) u=a;
			if (v<a+b) v=r0;
		}
	}
}
### 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>
using namespace std;
typedef long long ll;
int main()
{
	ll a,b;
	cin>>b>>a;
	ll r0=a+b*2-1;
	ll s1=(a+r0)*b;
	ll s2=(r0+1+r0+b)*b/2;
	//cout<<s1<<' '<<s2<<endl;
	ll ans;
	if (s1>s2) {
		cout<<-1<<endl;
		return 0;
	}
	else
	{
		ll u=a+1,v;
		if (b%2==1)
		   v=r0-b/2-1;
		else v=r0-b/2;
		for (ll i=r0+1;i<=r0+b;i++)
		{
			cout<<u<<' '<<v--<<' ';
			cout<<i<<endl;
			u+=2;
			if (u>=a+b) u=a;
			if (v<a+b) v=r0;
		}
	}
}
```