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>
#include<cstdio>
#include<stack>
#include<queue>
#include<algorithm>
#include<string>
#include<set>
#include<map>
#include<vector>
#include<math.h>
using namespace std; 
#define sim template < class c
#define ris return * this
#define dor > debug & operator <<
#define eni(x) sim > typename \
  enable_if<sizeof dud<c>(0) x 1, debug&>::type operator<<(c i) {
sim > struct rge { c b, e; };
sim > rge<c> range(c i, c j) { return rge<c>{i, j}; }
sim > auto dud(c* x) -> decltype(cerr << *x, 0);
sim > char dud(...);
struct debug {
#ifdef LOCAL
~debug() { cerr << endl; }
eni(!=) cerr << boolalpha << i; ris; }
eni(==) ris << range(begin(i), end(i)); }
sim, class b dor(pair < b, c > d) {
  ris << "(" << d.first << ", " << d.second << ")";
}
sim dor(rge<c> d) {
  *this << "[";
  for (auto it = d.b; it != d.e; ++it)
    *this << ", " + 2 * (it == d.b) << *it;
  ris << "]";
}
#else
sim dor(const c&) { ris; }
#endif
};
#define pp(...) "\033[94m [" << #__VA_ARGS__ ": " << (__VA_ARGS__) << "] "
#define dg1(x) debug() << pp(x)
#define dg2(x,y) debug() << pp(x) pp(y)
#define dg3(x,y,z) debug() << pp(x) pp(y) pp(z)
#define dg4(w,x,y,z) debug() << pp(w) pp(x) pp(y) pp(z)
#define msg(x) debug() << x
#define int long long
const int xx = 2e5;
const int MOD = 1e9 + 7;
bool cmp(const pair<int,int>&a , const pair<int,int>&b){
  if(a.second != b.second) return a.second < b.second;
  return a.first < b.first;
}
signed main(){
  ios::sync_with_stdio(false);cin.tie(0);
  int n , k;
  cin >> n >> k;
  int edge = (n-1) * (n-2) / 2;
  if(k > edge){
    cout << -1 << '\n';
    return 0;
  }
  for(int i=2;i<=n;i++){
    cout << 1 <<" " << i << '\n';
  }
  for(int i=2;i<=n-1;i++){
    for(int j = i + 1;j<=n;j++){
      if(edge == k) return 0;
      cout << i <<" " << j << '\n';
      edge--;
    }
  }
}