#include <algorithm>
#include <iostream>
#include <cstdio>
#include <vector>
#include <cmath>
#include <queue>
#include <stack>
using namespace std;
typedef long long lli;
typedef pair<int, int> pii;
const int maxn = 1e5 + 5;
int n, k;
int a[maxn][3];

void ReadInput()
{
    cin >> n >> k;
}

void Solve()
{
    for(int i = 0; i < n; ++i)
    {
        a[i][2] = k + 3 * n - i - 1;
        if(2 * i < n)
        {
            a[i][0] = k + n / 2 + i;
            a[i][1] = k + 2 * n - 1 - 2 * i;
        }
        else
        {
            int p = (2 * i - n) / 2;
            a[i][0] = k + p;
            a[i][1] = k + 2 * n - 2 - 2 * p;
        }
    }

    for(int i = 0; i < n; ++i)
        if(a[i][0] + a[i][1] > a[i][2])
        {
            cout << "-1\n";
            return;
        }

    for(int i = 0; i < n; ++i)
        cout << a[i][0] << ' ' << a[i][1] << ' ' << a[i][2] << '\n';
}

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

### 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 <algorithm>
#include <iostream>
#include <cstdio>
#include <vector>
#include <cmath>
#include <queue>
#include <stack>
using namespace std;
typedef long long lli;
typedef pair<int, int> pii;
const int maxn = 1e5 + 5;
int n, k;
int a[maxn][3];

void ReadInput()
{
    cin >> n >> k;
}

void Solve()
{
    for(int i = 0; i < n; ++i)
    {
        a[i][2] = k + 3 * n - i - 1;
        if(2 * i < n)
        {
            a[i][0] = k + n / 2 + i;
            a[i][1] = k + 2 * n - 1 - 2 * i;
        }
        else
        {
            int p = (2 * i - n) / 2;
            a[i][0] = k + p;
            a[i][1] = k + 2 * n - 2 - 2 * p;
        }
    }

    for(int i = 0; i < n; ++i)
        if(a[i][0] + a[i][1] > a[i][2])
        {
            cout << "-1\n";
            return;
        }

    for(int i = 0; i < n; ++i)
        cout << a[i][0] << ' ' << a[i][1] << ' ' << a[i][2] << '\n';
}

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

```