#include <iostream>

using namespace std;

int main()
{
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);

    int n, k; cin >> n >> k; --k;
    if(((n - 1) >> 1) < k) {cout << -1; return 0;}

    int l = 1, r = (n << 1) - (n >> 1), b = (n << 1) + 1;
    while(l <= n) {cout << l + k << ' ' << r + k << ' ' << b + k << '\n'; l += 2; --r; ++b;}
    l = 2, r = (n << 1);
    while(l <= n) {cout << l + k << ' ' << r + k << ' ' << b + k << '\n'; l += 2; --r; ++b;}
    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 <iostream>

using namespace std;

int main()
{
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);

    int n, k; cin >> n >> k; --k;
    if(((n - 1) >> 1) < k) {cout << -1; return 0;}

    int l = 1, r = (n << 1) - (n >> 1), b = (n << 1) + 1;
    while(l <= n) {cout << l + k << ' ' << r + k << ' ' << b + k << '\n'; l += 2; --r; ++b;}
    l = 2, r = (n << 1);
    while(l <= n) {cout << l + k << ' ' << r + k << ' ' << b + k << '\n'; l += 2; --r; ++b;}
    return 0;
}

```