Problem:
Score: 500 points

Problem Statement

Does there exist an undirected graph with N vertices satisfying the following conditions?

The graph is simple and connected.

The vertices are numbered 1, 2, ..., N.

Let M be the number of edges in the graph. The edges are numbered 1, 2, ..., M, the length of each edge is 1, and Edge i connects Vertex u_i and Vertex v_i.

There are exactly K pairs of vertices (i,\ j)\ (i < j) such that the shortest distance between them is 2.

If there exists such a graph, construct an example.

Constraints

All values in input are integers.

2 \leq N \leq 100

0 \leq K \leq \frac{N(N - 1)}{2}

Input

Input is given from Standard Input in the following format:

N K

Output

If there does not exist an undirected graph with N vertices satisfying the conditions, print -1.

If there exists such a graph, print an example in the following format (refer to Problem Statement for what the symbols stand for):

M
u_1 v_1
:
u_M v_M

If there exist multiple graphs satisfying the conditions, any of them will be accepted.

Sample Input 1

5 3

Sample Output 1

5
4 3
1 2
3 1
4 5
2 3

This graph has three pairs of vertices such that the shortest distance between them is 2: (1,\ 4), (2,\ 4), and (3,\ 5). Thus, the condition is satisfied.

Sample Input 2

5 8

Sample Output 2

-1

There is no graph satisfying the conditions.

Solution in C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <bits/stdc++.h>

using namespace std;
typedef long long ll;
#define all(x) (x).begin(),(x).end()
#define REP(i,N) for(int i=0;i<N;i++)

int main()
{
    int n,k; cin>>n>>k;
    if((n-2)*(n-1)/2<k){
        cout<<-1<<endl;
        return 0;
    }

    int m = (n-2)*(n-1)/2 - k;
    cout<<n-1+m<<endl;
    for(int i=2;i<=n;i++){
        cout<<"1 "<<i<<endl;
    }
    int src = 2;
    int dst = 3;
    for(int i=0;i<m;i++){
        cout<<src<<" "<<dst<<endl;
        dst++;
        if(dst>n){
            src++; dst=src+1;
        }
    }

    return 0;
}