#include <cstdio>
#define Maxn 100000
int k,n;
int ans[Maxn+5][3];
int main(){
	scanf("%d%d",&n,&k);
	if(n<2*k-1){
		puts("-1");
		return 0;
	}
	int len=0;
	for(int i=0;i<n/2;i++){
		ans[++len][0]=k+n/2-1-i;
		ans[len][1]=k+n+i*2+1;
		ans[len][2]=k+n*2+i;
	}
	for(int i=0;i<(n+1)/2;i++){
		ans[++len][0]=k+n-1-i;
		ans[len][1]=k+n+i*2;
		ans[len][2]=k+n*2+n/2+i;
	}
	for(int i=1;i<=len;i++){
		printf("%d %d %d\n",ans[i][0],ans[i][1],ans[i][2]);
	}
	return 0;
}

### Prompt

Generate 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>
#define Maxn 100000
int k,n;
int ans[Maxn+5][3];
int main(){
	scanf("%d%d",&n,&k);
	if(n<2*k-1){
		puts("-1");
		return 0;
	}
	int len=0;
	for(int i=0;i<n/2;i++){
		ans[++len][0]=k+n/2-1-i;
		ans[len][1]=k+n+i*2+1;
		ans[len][2]=k+n*2+i;
	}
	for(int i=0;i<(n+1)/2;i++){
		ans[++len][0]=k+n-1-i;
		ans[len][1]=k+n+i*2;
		ans[len][2]=k+n*2+n/2+i;
	}
	for(int i=1;i<=len;i++){
		printf("%d %d %d\n",ans[i][0],ans[i][1],ans[i][2]);
	}
	return 0;
}

```