#include <iostream>
using namespace std;
int main() {
    int n, k; cin >> n >> k;
    if (k > (n + 1) / 2) { cout << "-1\n"; return 0; }
    for (int a = 0, b = n + (n + 1) / 2, c = 2 * n + 1; a < n; a++, b++, c += 2) {
        if (b >= 2 * n) { b = n; c = 2 * n; }
        cout << a + k << ' ' << b + k << ' ' << c + k << endl;
    }
}

### Prompt

Please provide a cpp coded solution 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>
using namespace std;
int main() {
    int n, k; cin >> n >> k;
    if (k > (n + 1) / 2) { cout << "-1\n"; return 0; }
    for (int a = 0, b = n + (n + 1) / 2, c = 2 * n + 1; a < n; a++, b++, c += 2) {
        if (b >= 2 * n) { b = n; c = 2 * n; }
        cout << a + k << ' ' << b + k << ' ' << c + k << endl;
    }
}

```