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)

//↓template↓

#include "bits/stdc++.h"
using namespace std;
#define Would
#define you
#define all(n)  n.begin(),n.end()
#define rall(n) n.rbegin(),n.rend()
typedef long long ll;
const ll INF = 1e18;
const ll MOD = 1e9 + 7;
const double pi = acos(-1);
const ll SIZE = 1 << 17;
int dx[] = { 1,0,-1,0 }, dy[] = { 0,1,0,-1 }, alp[30];
ll fac[200005], finv[200005], inv[200005];
vector<ll>dij;
struct edge { ll to, cost; };
vector<vector<edge> >G;

ll mod_pow(ll a, ll b) {
	ll res = 1, mul = a;
	for (int i = 0; i < 31; ++i) {
		if (b >> i & 1) {
			res *= mul;
			res %= MOD;
		}
		mul = (mul * mul) % MOD;
	}

	return res;
}

void addedge(int from, int to, int cost) {
	G[from].push_back({ to,cost });
	G[to].push_back({ from,cost });
}


template<typename T>
vector<T> make_v(size_t a) { return vector<T>(a); }

template<typename T, typename... Ts>
auto make_v(size_t a, Ts... ts) {
	return vector<decltype(make_v<T>(ts...))>(a, make_v<T>(ts...));
}

template<typename T, typename V>
typename enable_if<is_class<T>::value == 0>::type
fill_v(T &t, const V &v) { t = v; }

template<typename T, typename V>
typename enable_if<is_class<T>::value != 0>::type
fill_v(T &t, const V &v) {
	for (auto &e : t) fill_v(e, v);
}

template<typename T>
void outp(vector<T>v) {
	for (int i = 0; i < v.size(); ++i) {
		cout << v[i];
		if (i != v.size() - 1) { cout << " "; }
	}
}

//↑template↑


int main() {
	int a, b;
	cin >> a >> b;
	if (b > ((a - 1)*(a - 2)) / 2) { cout << -1 << endl; return 0; }

	int ans = a - 1 + (a - 1)*(a - 2) / 2 - b;
	cout << ans << endl;
	for (int i = 0; i < a - 1; ++i) {
		cout << 1 << " " << i + 2 << endl;
	}

	for (int i = 0; i < ans - a + 1; ++i) {
		cout << i + 2 << " " << i + 3 << endl;
	}
}