#include<bits/stdc++.h>

int main(){
    using namespace std;
    unsigned long N, K;
    cin >> N >> K;
    if(2 * K > N + 1)return 0 & puts("-1");
    unsigned long k_1 = N / 2, k_2 = (N + 1) / 2;
    for(unsigned long i = K, j = K + 2 * N; i < K + k_2; ++i, j += 2){
        cout << i << " " << i + k_1 + N << " " << j << endl;
    }
    for(unsigned long i = K + k_2, j = K + 2 * N + 1; i < K + N; ++i, j += 2){
        cout << i << " " << i - k_2 + N << " " << j << endl;
    }
    return 0;
}
### Prompt

Please formulate 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<bits/stdc++.h>

int main(){
    using namespace std;
    unsigned long N, K;
    cin >> N >> K;
    if(2 * K > N + 1)return 0 & puts("-1");
    unsigned long k_1 = N / 2, k_2 = (N + 1) / 2;
    for(unsigned long i = K, j = K + 2 * N; i < K + k_2; ++i, j += 2){
        cout << i << " " << i + k_1 + N << " " << j << endl;
    }
    for(unsigned long i = K + k_2, j = K + 2 * N + 1; i < K + N; ++i, j += 2){
        cout << i << " " << i - k_2 + N << " " << j << endl;
    }
    return 0;
}
```