#include <iostream>
#include <algorithm>
#include <string>
#include <vector>
#include <cmath>
#include <map>
#include <queue>
#include <iomanip>
#include <set>
#include <tuple>
#define mkp make_pair
#define mkt make_tuple
#define rep(i,n) for(int i = 0; i < (n); ++i)
using namespace std;
typedef long long ll;
const ll MOD=1e9+7;

ll N;
ll K;


int main(){
  cin>>N>>K;
  
  ll ab=2*N*(K+K+2*N-1)/2;
  ll c=N*(K+2*N+K+3*N-1)/2;
  if(ab>c){
      cout<<-1<<endl;
      return 0;
  }

  vector<ll> A(N),B(N),C(N);
  int ind=0;
  ll p=N+N/2;
  for(ll i=0;i<N;i++){
      if(K+i+p<K+2*N){
          A[i]=K+i;
          B[i]=K+p+i;
      }else{
          A[i]=K+i;
          B[i]=K+N+ind;
          ind++;
      }
      C[i]=A[i]+B[i];
  }

  vector<pair<ll,int>> v;
  rep(i,N) v.push_back(mkp(C[i],i));
  sort(v.begin(),v.end());
  for(int i=0;i<N;i++){
      int now=v[i].second;
      cout<<A[now]<<" "<<B[now]<<" "<<K+2*N+i<<endl;
  }

  return 0;
}

### Prompt

Create a solution in CPP for 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 <algorithm>
#include <string>
#include <vector>
#include <cmath>
#include <map>
#include <queue>
#include <iomanip>
#include <set>
#include <tuple>
#define mkp make_pair
#define mkt make_tuple
#define rep(i,n) for(int i = 0; i < (n); ++i)
using namespace std;
typedef long long ll;
const ll MOD=1e9+7;

ll N;
ll K;


int main(){
  cin>>N>>K;
  
  ll ab=2*N*(K+K+2*N-1)/2;
  ll c=N*(K+2*N+K+3*N-1)/2;
  if(ab>c){
      cout<<-1<<endl;
      return 0;
  }

  vector<ll> A(N),B(N),C(N);
  int ind=0;
  ll p=N+N/2;
  for(ll i=0;i<N;i++){
      if(K+i+p<K+2*N){
          A[i]=K+i;
          B[i]=K+p+i;
      }else{
          A[i]=K+i;
          B[i]=K+N+ind;
          ind++;
      }
      C[i]=A[i]+B[i];
  }

  vector<pair<ll,int>> v;
  rep(i,N) v.push_back(mkp(C[i],i));
  sort(v.begin(),v.end());
  for(int i=0;i<N;i++){
      int now=v[i].second;
      cout<<A[now]<<" "<<B[now]<<" "<<K+2*N+i<<endl;
  }

  return 0;
}

```