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: Accepted)

#pragma region include
#include <iostream>
#include <vector>
#include <algorithm>
#include <map>
#include <string>
#include <queue>
#include <stack>
#include <cmath>
#include <set>
#include <cstdio>
#include <tuple>
#define ALL(obj) (obj).begin(),(obj).end()
#define RALL(obj) (obj).rbegin(),(obj).rend()
#define REP(i, n) for(int i = 0; i < (int)(n); i++)
#define REPR(i, n) for(int i = (int)(n); i >= 0; i--)
#define FOR(i,n,m) for(int i = (int)(n); i < int(m); i++)
#define MOD (1e9+7)
#define INF (1e9)
#define LLINF (4e18)
using namespace std;
typedef long long ll;
typedef pair<int, int> PII;
typedef vector<int> VI;
typedef vector<VI> VVI;
void input() {}
template<typename... R> void input(int& f, R&... r) { scanf("%d", &f); input(r...); }
template<typename... R> void input(double& f, R&... r) { scanf("%lf", &f); input(r...); }
template<typename... R> void input(ll& f, R&... r) { scanf("%lld", &f); input(r...); }
template<typename... R> void input(char& f, R&... r) { scanf("%c", &f); input(r...); }
template<typename... R> void input(string& f, R&... r) { cin >> f; input(r...); }
template<typename T, typename... R> void input(vector<T>& f, R&... r) { REP(i, f.size())input(f[i]); input(r...); }
#pragma endregion

int main() {
    int N, K; input(N, K);
    if ((N - 1)*(N - 2) / 2 < K) cout << -1 << endl;
    else {
        vector<int> u, v;
        REP(i, N - 1) {
            u.emplace_back(1);
            v.emplace_back(i + 2);
        }
        int t = (N - 1)*(N - 2) / 2 - K;
        // t個消す
        if (t != 0) {
            FOR(i, 2, N) {
                FOR(j, i + 1, N + 1) {
                    u.emplace_back(i);
                    v.emplace_back(j);
                    t--;
                    if (t <= 0) break;
                }
                if (t <= 0) break;
            }
        }
        cout << u.size() << endl;
        REP(i, u.size()) {
            cout << u[i] << " " << v[i] << endl;
        }
    }
    getchar(); getchar();
}