#include<iostream>
#include<string>
#include<algorithm>
#include<vector>
#include<iomanip>
#include<math.h>
#include<complex>
#include<queue>
#include<deque>
#include<stack>
#include<map>
#include<set>
#include<bitset>
#include<functional>
#include<assert.h>
#include<numeric>
using namespace std;
#define REP(i,m,n) for(int i=(int)(m) ; i < (int) (n) ; ++i )
#define rep(i,n) REP(i,0,n)
using ll = long long;
const int inf=1e9+7;
const ll longinf=1LL<<60 ;
const ll mod=1e9+7 ;

int main(){
    ll n,k;
    cin>>n>>k;
    ll mi = (k+(k+2*n-1))*n;
    ll ma = (k+2*n+k+3*n-1)*n/2;
    if(mi>ma){
        cout<<-1<<endl;
        return 0;
    }
    vector<int> a(2*n),c(n);
    rep(i,2*n){
        if(i%2)a[i] = i/2+k;
        else a[i] = i/2+k+n;
    }
    if(n%2==0){
        rep(i,n){
            if(i%2==0)a[i]-=n;
            else a[i]+=n;
        }
    }
    rep(i,n)c[i]=k+2*n+i;
    rep(i,n){
        //assert(c[i]>=a[i]+a[i+n]);
        cout<<a[i]<<" "<<a[i+n]<<" "<<c[i]<<endl;
    }
    return 0;
}
### Prompt

Your challenge is to write 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<string>
#include<algorithm>
#include<vector>
#include<iomanip>
#include<math.h>
#include<complex>
#include<queue>
#include<deque>
#include<stack>
#include<map>
#include<set>
#include<bitset>
#include<functional>
#include<assert.h>
#include<numeric>
using namespace std;
#define REP(i,m,n) for(int i=(int)(m) ; i < (int) (n) ; ++i )
#define rep(i,n) REP(i,0,n)
using ll = long long;
const int inf=1e9+7;
const ll longinf=1LL<<60 ;
const ll mod=1e9+7 ;

int main(){
    ll n,k;
    cin>>n>>k;
    ll mi = (k+(k+2*n-1))*n;
    ll ma = (k+2*n+k+3*n-1)*n/2;
    if(mi>ma){
        cout<<-1<<endl;
        return 0;
    }
    vector<int> a(2*n),c(n);
    rep(i,2*n){
        if(i%2)a[i] = i/2+k;
        else a[i] = i/2+k+n;
    }
    if(n%2==0){
        rep(i,n){
            if(i%2==0)a[i]-=n;
            else a[i]+=n;
        }
    }
    rep(i,n)c[i]=k+2*n+i;
    rep(i,n){
        //assert(c[i]>=a[i]+a[i+n]);
        cout<<a[i]<<" "<<a[i+n]<<" "<<c[i]<<endl;
    }
    return 0;
}
```