#include<iostream>
#include<cstdio>
#include<algorithm>
#include<cmath>
#include<vector>
#include<map>
#include<set>
#include<string>
#include<queue>
#include<stack>
using namespace std;
#define MOD 1000000007
#define INF (1<<29)
#define LINF (1LL<<60)
#define EPS (1e-10)
typedef long long Int;
typedef pair<Int, Int> P;
typedef pair<Int, P> T;
Int n, k, a, b, c;

int main(){
    cin >> n >> k;
    if(n < 2 * k - 1){
        cout << -1 << endl;
        return 0;
    }
    int middle =  n / 2;
    vector<T> nums;
    for(int i = 0;i < n;i++){
        a = i+k;
        b = n + ((i+middle) % n) + k;
        nums.push_back(T(a+b,P(a, b)));
    }
    sort(nums.begin(), nums.end());
    for(int i = 0;i < n;i++){
        Int a = nums[i].second.first;
        Int b = nums[i].second.second;
        Int c = n + n + i + k;
        cout << a << " " << b << " "<< c << endl;
    }
    return 0;
}
### Prompt

Your task is to create 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>
#include<cstdio>
#include<algorithm>
#include<cmath>
#include<vector>
#include<map>
#include<set>
#include<string>
#include<queue>
#include<stack>
using namespace std;
#define MOD 1000000007
#define INF (1<<29)
#define LINF (1LL<<60)
#define EPS (1e-10)
typedef long long Int;
typedef pair<Int, Int> P;
typedef pair<Int, P> T;
Int n, k, a, b, c;

int main(){
    cin >> n >> k;
    if(n < 2 * k - 1){
        cout << -1 << endl;
        return 0;
    }
    int middle =  n / 2;
    vector<T> nums;
    for(int i = 0;i < n;i++){
        a = i+k;
        b = n + ((i+middle) % n) + k;
        nums.push_back(T(a+b,P(a, b)));
    }
    sort(nums.begin(), nums.end());
    for(int i = 0;i < n;i++){
        Int a = nums[i].second.first;
        Int b = nums[i].second.second;
        Int c = n + n + i + k;
        cout << a << " " << b << " "<< c << endl;
    }
    return 0;
}
```