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 int long long
using namespace std;
#define rep(i, n) for(int i=0;i<(n);++i)
typedef pair<int, int> pii;
const int INF = 1l << 60;
#define u_b upper_bound
#define l_b lower_bound

int N, K;
bool enable[110];

signed main() {
    cin >> N >> K;
    //辺は最低N-1本
    if (N * (N - 1) / 2 - (N - 1) < K) {
        cout << -1 << endl;
    }
    int M = N * (N - 1) / 2;
    vector<pii> E;
    for (int i = 1; i <= N; ++i) {
        for (int j = i + 1; j <= N; ++j) {
            E.push_back(pii(i, j));
        }
    }
    int k = 0;
    cout << M - K << endl;
    for (pii e:E) {
        if (e.first == 1) {
            cout << e.first << " " << e.second << endl;
        } else if (k == K) {
            cout << e.first << " " << e.second << endl;
        } else {
            k++;
        }
    }
    return 0;
}