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: Runtime Error)


#include <iostream>
#include <iomanip>
#include <cstdio>
#include <string>
#include <cstring>
#include <deque>
#include <list>
#include <queue>
#include <stack>
#include <vector>
#include <utility>
#include <algorithm>
#include <map>
#include <set>
#include <complex>
#include <cmath>
#include <limits>
#include <cfloat>
#include <climits>
#include <ctime>
#include <cassert>
#include <numeric>
#include <fstream>
#include <functional>
#include <bitset>

using namespace std;
#define int long long int
const int INF = 1001001001001001LL;
const int MOD = 1000000007;

int di[] = {-1, 0, 1, 0, -1, 1, 1, -1};
int dj[] = {0, 1, 0, -1, 1, 1, -1, -1};

signed main(){
    
    int n, k; cin >> n >> k;
    int num = (n - 1) * (n - 2) / 2;
    if(k > num){
        cout << -1 << endl;
        return 0;
    }
    int e = 0;
    vector<vector<int>> g(n, vector<int> (n, 0));
    if(k <= n){
        for(int i = 0; i < n; i++){
            int u = i;
            int v = (i + 1) % n;
            g[u][v] = 1;
            e++;
        }
        
        int add = n - k;
        for(int i = 0; i < add; i++){
            int u = i;
            int v = (i + 2) % n;
            g[u][v] = 1;
            e++;
        }

    }else{
        for(int i = 1; i < n; i++){
            g[0][i] = 1;
            e++;
        }

        int add = num - k;
        for(int i = 0; i < add; i++){
            int u = 1;
            int v = i + 3;
            if(v >= n) v -= (n - 1);
            g[u][v] = 1;
            e++;
        }
    }

    cout << e << endl;
    for(int i = 0; i < n; i++){
        for(int j = 0; j < n; j++){
            if(g[i][j]) cout << i + 1 << " " << j + 1 << endl;
       }
    }

    return 0;
}