#include <bits/stdc++.h>
using namespace std;
void print(int a,int b,int c){cout << a << ' ' << b << ' ' << c << '\n';}

int main(){
    cin.tie(0);
    ios::sync_with_stdio(false);
    int N,K; cin >> N >> K;
    if (N+1<2*K){cout << -1 << '\n'; return 0;}
    for (int i=0;i<K;++i) print(K+i,2*N+i,K+2*N+2*i);
    for (int i=0;i<K-1;++i) print(2*K+i,-K+2*N+1+i,K+2*N+1+2*i);
    for (int i=0;i<N-2*K+1;++i) print(3*K-1+i,-K+2*N-i,3*K+2*N-1+i);
}
### Prompt

In Cpp, your task is to solve 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 <bits/stdc++.h>
using namespace std;
void print(int a,int b,int c){cout << a << ' ' << b << ' ' << c << '\n';}

int main(){
    cin.tie(0);
    ios::sync_with_stdio(false);
    int N,K; cin >> N >> K;
    if (N+1<2*K){cout << -1 << '\n'; return 0;}
    for (int i=0;i<K;++i) print(K+i,2*N+i,K+2*N+2*i);
    for (int i=0;i<K-1;++i) print(2*K+i,-K+2*N+1+i,K+2*N+1+2*i);
    for (int i=0;i<N-2*K+1;++i) print(3*K-1+i,-K+2*N-i,3*K+2*N-1+i);
}
```