#include <utility>
#include <iostream>
#include <cmath>
#include <deque>
#include <string>
#include <time.h>
#include <stack>
#include <vector>
#include <map>
#include <set>
#include <sstream>
#include <algorithm>
#include <bitset>

#define pii pair<ll,ll>
#define X first
#define Y second
#define mp make_pair

typedef long long ll;
using namespace std;
#define MAXN 10000007
#define MOD 998244353
#define N 1048576
ll n, x, k, z, m, pos, q, ans_v, y;
ll x1, p1, x2;
ll d[100500];
ll c[100500];
vector<ll> rem[100500];
vector<pii> g[100500];
multiset<ll> f;

int main() {
    cin >> n >> k;
    if (n < k * 2 - 1) {
        cout << -1 << endl;
        return 0;
    }

    for (int i = 0; i < n; i++) {
        cout << i / 2 + k + (i % 2) * n << " " << (i + n) / 2 + k + ((i+1) % 2) * n << " " << k + 2 * n + i << "\n";
    }
    return 0;
}
### Prompt

Develop a solution in cpp 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 <utility>
#include <iostream>
#include <cmath>
#include <deque>
#include <string>
#include <time.h>
#include <stack>
#include <vector>
#include <map>
#include <set>
#include <sstream>
#include <algorithm>
#include <bitset>

#define pii pair<ll,ll>
#define X first
#define Y second
#define mp make_pair

typedef long long ll;
using namespace std;
#define MAXN 10000007
#define MOD 998244353
#define N 1048576
ll n, x, k, z, m, pos, q, ans_v, y;
ll x1, p1, x2;
ll d[100500];
ll c[100500];
vector<ll> rem[100500];
vector<pii> g[100500];
multiset<ll> f;

int main() {
    cin >> n >> k;
    if (n < k * 2 - 1) {
        cout << -1 << endl;
        return 0;
    }

    for (int i = 0; i < n; i++) {
        cout << i / 2 + k + (i % 2) * n << " " << (i + n) / 2 + k + ((i+1) % 2) * n << " " << k + 2 * n + i << "\n";
    }
    return 0;
}
```