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 <iostream>
#include <vector>

using namespace std;

int main(void) {
    int N, K;
    cin >> N >> K;
    int X = (N-1)*(N-2) / 2 - K;
    vector< pair<int,int> > p;
    if(X < 0) {
        cout << -1 << endl;
        return 0;

    } else {
        for(int i=2; i<=N; i++) {
            p.push_back(make_pair(1, i));
        }
        for(int i=2; i<=N; i++) {
            for(int j=i+1; j<=N; j++) {
                if(X != 0) {
                    p.push_back(make_pair(i, j));
                    X--;
                } else {
                    break;
                }
            }
        }
    }
    cout << p.size() << endl;
    for(auto &x : p) {
        cout << x.first << " " << x.second << endl;
    }
    return 0;

}