#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
ll n,k;
int main()
{
    scanf("%lld%lld",&n,&k);
    if(2*k<=n+1)
    {
        k--;
        for(int i=1;i<=n/2+n%2;i++)
            printf("%lld %lld %lld\n",k+n-(i-1)*2,k+n+n/2+i,k+3*n-i+1);
        for(int i=1;i<=n/2;i++)
            printf("%lld %lld %lld\n",k+n-1-(i-1)*2,k+n+i,k+2*n+n/2-i+1);
        return 0;
    }
    else printf("-1\n");
}

### 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<bits/stdc++.h>
using namespace std;
typedef long long ll;
ll n,k;
int main()
{
    scanf("%lld%lld",&n,&k);
    if(2*k<=n+1)
    {
        k--;
        for(int i=1;i<=n/2+n%2;i++)
            printf("%lld %lld %lld\n",k+n-(i-1)*2,k+n+n/2+i,k+3*n-i+1);
        for(int i=1;i<=n/2;i++)
            printf("%lld %lld %lld\n",k+n-1-(i-1)*2,k+n+i,k+2*n+n/2-i+1);
        return 0;
    }
    else printf("-1\n");
}

```