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 <bits/stdc++.h>
#define _ ios_base::sync_with_stdio(false);cin.tie(NULL);cout.tie(NULL);
#define int long long
#define pb insert
#define sz(i) (int)(i.size())
#define F first
#define S second
#define L long double
#define P pair<int, int>
const int inf = 0x3f3f3f3f3f3f3f3LL;
const int mod = (int)1e9 + 7;
using namespace std;
#if LOCAL
#include "../../tr.h"
#else
#define tr(...)
#define endl '\n'
#endif
template<class T> void smin(T& a, T val) {if (a > val) a = val;}template<class T> void smax(T& a, T val) {if (a < val) a = val;}
const int N = 5*(int)1e5 + 10;

int n, k;
set<P> v;

int32_t main(){_

   cin>>n>>k;

   int ma = (n-2) * (n-1) / 2;
   
   if (k <= 0){
      cout<<-1;
      exit(0);
   }

   if (k > ma){
      cout<<-1;
      exit(0);
   }

   int vals = 0;
   for (int adj = 1; adj <= n; ++adj)
   {
      int tot = adj - 1;
      tot = tot * (tot+1);
      tot >>= 1;
      if(tot <= k){
         vals = adj;
      }
      else{
         break;
      }
   }

   int adj = vals;

   for (int i = 1; i <= adj; ++i)
   {
      v.pb({1, i+1});
   }

   k -= ((adj * (adj - 1)) / 2);

   adj+=2;
   int lst = adj;
   tr(adj, k, v);
   for (int i = adj; i <= n; ++i)
   {
      int poss = adj-2;
      if(k > 0 and k - poss < 0){
         v.pb({i, 1});
         int rem = k;
         k = 0;
         for (int j = 2; j <= adj-rem-1; ++j)
         {
            v.pb({i, j});            
         }
         lst = adj+1;
         break;
      }
   }

   tr(lst, k);

   for (int i = lst; i <= n; ++i)
   {
      for (int j = 1; j <= i-1; ++j)
      {
         v.pb({i, j});
      }
   }

   if(k > 0){
      assert(0);
      cout<<-1;
      exit(0);
   }

   cout<<sz(v)<<endl;
   for(auto it: v)
      cout<<it.F<<' '<<it.S<<endl;


   return 0;
}