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++ (GCC 9.2.1) (judge verdict: Wrong Answer)

#include <iostream>
#include <utility>
#include <map>
#include <vector>
#include <algorithm>
#include <queue>
#include <math.h>
#include <stack>
#include <set>
#include <deque>
#include <cmath>

using namespace std;
typedef long long ll;
ll mod = 1e9+7;
//ll mod = 998244353;
#define rep(i,n) for(int i = 0; i < (n); ++i)

int main() {
    int n, k;
    cin >> n >> k;
    int max_num = n * (n - 1) / 2 - (n - 1);
    if (k > max_num) {
        cout << -1 << endl;
        return 0;
    }
    int rest = max_num - k;
    vector<pair<int, int>> ans;
    for (int i = 1; i < n; ++i) { 
        ans.push_back(make_pair(0, i+1));
    }
    //cout << max_num << " " << rest << endl;
    int cnt = 0;
    for (int i = 1; i < n; ++i) {
        bool flg = false;
        for (int j = i + 1; j < n; ++j) {
            ans.emplace_back(i, j);
            ++cnt;
            if (cnt == rest) {
                flg = true;
                break;
            }
        }
        if (flg) {
            break;
        }
    }
    //cout << (int)(ans.size()) << endl;
    for (auto a: ans) {
        cout << a.first + 1 << " " << a.second + 1 << endl;
    }
    return 0;
}