#include<iostream>
#include<algorithm>
#include<vector>
#include<queue>
#include<set>
#include<unordered_map>
using namespace std;
typedef long long ll;
#define chmax(a,b) a=max(a,b)
#define chmin(a,b) a=min(a,b)
#define mod 1000000007
#define mad(a,b) a=(a+b)%mod
#define N 100010
ll a[N],b[N],c[N];
int main(){
    cin.tie(0);
    ios::sync_with_stdio(0);
    ll n,k;
    cin>>n>>k;
    for(int i=1;i<=n;i++){
	a[i]=-1;
    }
    for(int i=0;i<n;i++){
	if(i<=(n-1)/2){
	    a[i*2]=i;
	    b[i*2]=i+n/2;
	}
    }
    ll p=(n-1)/2+1;
    for(int i=0;i<n;i++){
	if(a[i]>=0)continue;
	a[i]=p;
	b[i]=p-(n-n/2); 
	p++;
    }
    //for(int i=0;i<n/2;i++)swap(b[i],b[n-i-1]);
    for(int i=0;i<n;i++){
	a[i]+=k;
	b[i]+=k+n; //b[i]-=n;
	c[i]=k+n+n+i;
    }
    bool ok=1;
    for(int i=0;i<n;i++){
	if(a[i]+b[i]>c[i])ok=0;
    }
    if(ok==0)cout<<-1<<endl;
    else{
	for(int i=0;i<n;i++)cout<<a[i]<<" "<<b[i]<<" "<<c[i]<<endl;
    }
}


### Prompt

In CPP, your task is to solve 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<vector>
#include<queue>
#include<set>
#include<unordered_map>
using namespace std;
typedef long long ll;
#define chmax(a,b) a=max(a,b)
#define chmin(a,b) a=min(a,b)
#define mod 1000000007
#define mad(a,b) a=(a+b)%mod
#define N 100010
ll a[N],b[N],c[N];
int main(){
    cin.tie(0);
    ios::sync_with_stdio(0);
    ll n,k;
    cin>>n>>k;
    for(int i=1;i<=n;i++){
	a[i]=-1;
    }
    for(int i=0;i<n;i++){
	if(i<=(n-1)/2){
	    a[i*2]=i;
	    b[i*2]=i+n/2;
	}
    }
    ll p=(n-1)/2+1;
    for(int i=0;i<n;i++){
	if(a[i]>=0)continue;
	a[i]=p;
	b[i]=p-(n-n/2); 
	p++;
    }
    //for(int i=0;i<n/2;i++)swap(b[i],b[n-i-1]);
    for(int i=0;i<n;i++){
	a[i]+=k;
	b[i]+=k+n; //b[i]-=n;
	c[i]=k+n+n+i;
    }
    bool ok=1;
    for(int i=0;i<n;i++){
	if(a[i]+b[i]>c[i])ok=0;
    }
    if(ok==0)cout<<-1<<endl;
    else{
	for(int i=0;i<n;i++)cout<<a[i]<<" "<<b[i]<<" "<<c[i]<<endl;
    }
}


```