#include <iostream>
#include <algorithm>
#include <iomanip>
#include <vector>
#include <queue>
#include <set>
#include <map>

using namespace std;
typedef long long ll;

int main(){
    ios::sync_with_stdio(false);
    cin.tie(0);
    cout << setprecision(10) << fixed;
    ll N, K;
    cin >> N >> K;
    if(2*K-1 > N){
        cout << -1 << endl;
    }else{
        if(N%2 == 0){
            ll l = N/2;
            for(int i = 0; i < l; i++){
                cout << K+l-1-i << ' ' << K+2*l+2*i+1 << ' ' << K+2*N+i << endl;
            }
            for(int i = 0; i < l; i++){
                cout << K+2*l-i-1 << ' ' << K+2*l+2*i << ' ' << K+2*N+l+i << endl;
            }
        }else{
            ll l = (N-1)/2;
            for(int i = 0; i < l; i++){
                cout << K+l-1-i << ' ' << K+2*l+2*i+2 << ' ' << K+2*N+i << endl;
            }
            for(int i = 0; i <= l; i++){
                cout << K+2*l-i << ' ' << K+2*l+2*i+1 << ' ' << K+2*N+l+i << endl;
            }
        }
    }
}
### 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 <iostream>
#include <algorithm>
#include <iomanip>
#include <vector>
#include <queue>
#include <set>
#include <map>

using namespace std;
typedef long long ll;

int main(){
    ios::sync_with_stdio(false);
    cin.tie(0);
    cout << setprecision(10) << fixed;
    ll N, K;
    cin >> N >> K;
    if(2*K-1 > N){
        cout << -1 << endl;
    }else{
        if(N%2 == 0){
            ll l = N/2;
            for(int i = 0; i < l; i++){
                cout << K+l-1-i << ' ' << K+2*l+2*i+1 << ' ' << K+2*N+i << endl;
            }
            for(int i = 0; i < l; i++){
                cout << K+2*l-i-1 << ' ' << K+2*l+2*i << ' ' << K+2*N+l+i << endl;
            }
        }else{
            ll l = (N-1)/2;
            for(int i = 0; i < l; i++){
                cout << K+l-1-i << ' ' << K+2*l+2*i+2 << ' ' << K+2*N+i << endl;
            }
            for(int i = 0; i <= l; i++){
                cout << K+2*l-i << ' ' << K+2*l+2*i+1 << ' ' << K+2*N+l+i << endl;
            }
        }
    }
}
```