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: Wrong Answer)

#include <iostream> // cin, cout, cerr, clog
#include <algorithm> // minmax, sort, swap
#include <numeric> // iota, accumulate, inner_product
#include <cstdio> // printf, scanf
#include <climits> // INT_MIN, LLONG_MIN
#include <cmath> // long, trig, pow
#include <string> // string, stoi, to_string
#include <vector> // vector
#include <queue> // queue, priority_queue
#include <stack> // stack
#include <map> // key-value pairs sorted by keys
#include <set> // set
#include <unordered_map> // hashed by keys
#include <unordered_set> // hashed by keys
#include <iomanip> // cout<<setprecision(n)

#define rep(i,n) for(int i = 0; i < n; i++)
#define ENDL "\n"
#define print(i) std::cout << (i) << "\n"

#define int long long // at least int64 > 9*10^18
#define all(v) v.begin(), v.end()
struct FastIO
{
  FastIO() {
    std::cin.tie(0);
    std::ios_base::sync_with_stdio(0); 
  }
}fastio;

signed main() {
	int n,k;
	std::cin >> n >> k;
	if(k>(n-1)*(n-2)/2) {
		print(-1);
		return 0;
	}
	int diff = (n-1)*(n-2)/2-k;
	int m = n-1+diff;
	rep(i,n-1) std::cout << 0 << ' ' << i+1 << ENDL;
	int count = 0;
	for(int i = 1;i<n;i++) {
		for(int j=i+1;j<n;j++) {
			std::cout << i << ' ' << j << ENDL;
			count++;
			if(count>=diff) return 0;
		}
		if(i==n-1) return 0;
	}
  return 0;
}