#include <bits/stdc++.h>
using namespace std;

typedef long long ll;
typedef long double ld;
typedef pair<int, int> ii;
typedef pair<int, ii> iii;
typedef pair<ii, int> ri3;
#define mp make_pair
#define pb push_back
#define fi first
#define sc second
#define SZ(x) (int)(x).size()
#define ALL(x) begin(x), end(x) 
#define REP(i, n) for (int i = 0; i < n; ++i) 
#define FOR(i, a, b) for (int i = a; i <= b; ++i)
#define RFOR(i, a, b) for (int i = a; i >= b; --i)

int main() {
    //freopen("in.txt", "r", stdin);
    ios::sync_with_stdio(false);
    cin.tie(0);

    int N, K; cin >> N >> K;
    if (2*K-1 > N) cout << -1;
    else {
        vector<int> a, b, c;
        FOR(i,N,K+N-1) a.push_back(i);
        FOR(i,K,N-1) a.push_back(i);
        for(int i = K+2*N-1; i >= K+N; i -= 2) b.push_back(i);
        for(int i = K+2*N-2; i >= K+N; i -= 2) b.push_back(i);
        RFOR(i,K+3*N-1,K+2*N) c.push_back(i);
        FOR(i,0,N-1){
            cout << a[i] << " " << b[i] << " " << c[i] << '\n';
        }
    }
}


### 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 <bits/stdc++.h>
using namespace std;

typedef long long ll;
typedef long double ld;
typedef pair<int, int> ii;
typedef pair<int, ii> iii;
typedef pair<ii, int> ri3;
#define mp make_pair
#define pb push_back
#define fi first
#define sc second
#define SZ(x) (int)(x).size()
#define ALL(x) begin(x), end(x) 
#define REP(i, n) for (int i = 0; i < n; ++i) 
#define FOR(i, a, b) for (int i = a; i <= b; ++i)
#define RFOR(i, a, b) for (int i = a; i >= b; --i)

int main() {
    //freopen("in.txt", "r", stdin);
    ios::sync_with_stdio(false);
    cin.tie(0);

    int N, K; cin >> N >> K;
    if (2*K-1 > N) cout << -1;
    else {
        vector<int> a, b, c;
        FOR(i,N,K+N-1) a.push_back(i);
        FOR(i,K,N-1) a.push_back(i);
        for(int i = K+2*N-1; i >= K+N; i -= 2) b.push_back(i);
        for(int i = K+2*N-2; i >= K+N; i -= 2) b.push_back(i);
        RFOR(i,K+3*N-1,K+2*N) c.push_back(i);
        FOR(i,0,N-1){
            cout << a[i] << " " << b[i] << " " << c[i] << '\n';
        }
    }
}


```