#include <cstdio>
using namespace std;
int n,k;
int main(){
    scanf("%d%d",&k,&n);
    if ((k+1)/2<n){
        printf("-1\n");
        return 0;
    }

    int t;
    for (int x=0;x<k;x++){
        t=x/2;
        if (x&1) printf("%d %d %d\n",n+(k+1)/2+t,n+k+t,n+k*2+x);
        else printf("%d %d %d\n",n+t,n+k+k/2+t,n+k*2+x);
    }
}

### Prompt

Develop a solution in Cpp to the problem described below:

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>
using namespace std;
int n,k;
int main(){
    scanf("%d%d",&k,&n);
    if ((k+1)/2<n){
        printf("-1\n");
        return 0;
    }

    int t;
    for (int x=0;x<k;x++){
        t=x/2;
        if (x&1) printf("%d %d %d\n",n+(k+1)/2+t,n+k+t,n+k*2+x);
        else printf("%d %d %d\n",n+t,n+k+k/2+t,n+k*2+x);
    }
}

```