#include<iostream>
#include<cstdio>
#include<cstring>
#include<cmath>
#include<algorithm>
#include<queue>
#include<stack>
#include<vector>
#include<map>
#include<set>
using namespace std;
const int maxn = 1e6+10;
         
int read(){
   	int x=0,f=1;
   	char c=getchar();
   	while(!isdigit(c)){if(c=='-')f=-1;c=getchar();}
   	while(isdigit(c)){x=(x<<3)+(x<<1)+c-48;c=getchar();}
 	return x*f;
}
         
int k,m,n;
int a[maxn];
int main(){	
   	n=read();k=read();
   	long long sum=0,ans=0;
  	for(register int i=0;i<2*n;i++)sum+=k+i;
	for(register int i=2*n;i<3*n;i++)ans+=k+i;
  	if(ans<sum){puts("-1");return 0;}
	for(register int i=0;i<n*2;i++){
		if(i%2)a[i]=i/2+k;
		else a[i]=i/2+k+n;
	}
	if(n%2==0){
		for(register int i=0;i<n;i++){
			if(i%2==1)a[i]+=n;
			else a[i]-=n;
		}
	}
	for(register int i=0;i<n;i++)
		printf("%d %d %d\n",a[i],a[i+n],k+n*2+i);
  	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<iostream>
#include<cstdio>
#include<cstring>
#include<cmath>
#include<algorithm>
#include<queue>
#include<stack>
#include<vector>
#include<map>
#include<set>
using namespace std;
const int maxn = 1e6+10;
         
int read(){
   	int x=0,f=1;
   	char c=getchar();
   	while(!isdigit(c)){if(c=='-')f=-1;c=getchar();}
   	while(isdigit(c)){x=(x<<3)+(x<<1)+c-48;c=getchar();}
 	return x*f;
}
         
int k,m,n;
int a[maxn];
int main(){	
   	n=read();k=read();
   	long long sum=0,ans=0;
  	for(register int i=0;i<2*n;i++)sum+=k+i;
	for(register int i=2*n;i<3*n;i++)ans+=k+i;
  	if(ans<sum){puts("-1");return 0;}
	for(register int i=0;i<n*2;i++){
		if(i%2)a[i]=i/2+k;
		else a[i]=i/2+k+n;
	}
	if(n%2==0){
		for(register int i=0;i<n;i++){
			if(i%2==1)a[i]+=n;
			else a[i]-=n;
		}
	}
	for(register int i=0;i<n;i++)
		printf("%d %d %d\n",a[i],a[i+n],k+n*2+i);
  	return 0;
}
```