#include<bits/stdc++.h>
using namespace std;
const int N=1e5+5;
int n,k,i,a[N],b[N];
int main(){
	scanf("%d%d",&n,&k);
	if(k>n+1>>1){puts("-1");return 0;}
	for(i=0;i<n;++i)a[i]=i,b[i]=k+i+k+n+(i+(n-1>>1))%n;
	sort(a,a+n,[&](int x,int y){return b[x]<b[y];});
	for(i=0;i<n;++i){
		assert(k+a[i]+k+n+(a[i]+(n-1>>1))%n<=k+n*2+i);
		printf("%d %d %d\n",k+a[i],k+n+(a[i]+(n-1>>1))%n,k+n*2+i);
	}
}
### Prompt

Please formulate 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<bits/stdc++.h>
using namespace std;
const int N=1e5+5;
int n,k,i,a[N],b[N];
int main(){
	scanf("%d%d",&n,&k);
	if(k>n+1>>1){puts("-1");return 0;}
	for(i=0;i<n;++i)a[i]=i,b[i]=k+i+k+n+(i+(n-1>>1))%n;
	sort(a,a+n,[&](int x,int y){return b[x]<b[y];});
	for(i=0;i<n;++i){
		assert(k+a[i]+k+n+(a[i]+(n-1>>1))%n<=k+n*2+i);
		printf("%d %d %d\n",k+a[i],k+n+(a[i]+(n-1>>1))%n,k+n*2+i);
	}
}
```