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 <iostream>
#include<queue>
#include<vector>
#include<set>
#include<map>
#include<algorithm>
#include<cstring>
#include<string>
#include<cassert>
#include<cmath>
#include<climits>
#include<iomanip>

using namespace std;

#define MOD 1000000007
#define REP(i,n) for(ll (i)=0;(i)<(n);(i)++)
#define FOR(i,c) for(decltype((c).begin())i=(c).begin();i!=(c).end();++i)
#define ll long long
#define ull unsigned long long
#define all(hoge) (hoge).begin(),(hoge).end()
typedef pair<ll, ll> P;
const long long INF = 1LL << 60;
typedef vector<ll> Array;
typedef vector<Array> Matrix;


template<class T> inline bool chmin(T & a, T b) {
	if (a > b) {
		a = b;
		return true;
	}
	return false;
}
template<class T> inline bool chmax(T & a, T b) {
	if (a < b) {
		a = b;
		return true;
	}
	return false;
}


//グラフ関連
struct Edge {//グラフ
	ll to, cap, rev;
	Edge(ll _to, ll _cap, ll _rev) {
		to = _to; cap = _cap; rev = _rev;
	}
};
typedef vector<Edge> Edges;
typedef vector<Edges> Graph;
void add_edge(Graph& G, ll from, ll to, ll cap) {//最大フロー求める Ford-fulkerson
	G[from].push_back(Edge(to, cap, (ll)G[to].size()));
	G[to].push_back(Edge(from, cap, (ll)G[from].size() - 1));//最小カットの場合逆辺は0にする
}

ll max_flow_dfs(Graph & G, ll v, ll t, ll f, vector<bool> & used)
{
	if (v == t)
		return f;
	used[v] = true;
	for (int i = 0; i < G[v].size(); ++i) {
		Edge& e = G[v][i];
		if (!used[e.to] && e.cap > 0) {
			ll d = max_flow_dfs(G, e.to, t, min(f, e.cap), used);
			if (d > 0) {
				e.cap -= d;
				G[e.to][e.rev].cap += d;
				return d;
			}
		}
	}
	return 0;
}

ll max_flow(Graph & G, ll s, ll t)
{
	ll flow = 0;
	for (;;) {
		vector<bool> used(G.size());
		REP(i, used.size())used[i] = false;
		ll f = max_flow_dfs(G, s, t, INF, used);
		if (f == 0) {
			return flow;
		}
		flow += f;
	}
}

//最短経路(n>0だとだめ)
void Dijkstra(Graph& G, ll s, Array& d) {//O(|E|log|V|)
	d.resize(G.size());
	REP(i, d.size())d[i] = INF;
	d[s] = 0;
	priority_queue<P, vector<P>, greater<P>> q;
	q.push(make_pair(0, s));
	while (!q.empty()) {
		P a = q.top();
		q.pop();
		if (d[a.second] < a.first)continue;
		REP(i, G[a.second].size()) {
			Edge e = G[a.second][i];
			if (d[e.to] > d[a.second] + e.cap) {
				d[e.to] = d[a.second] + e.cap;
				q.push(make_pair(d[e.to], e.to));
			}
		}
	}
}

//最短経路(n<0でもok)
void WarshallFloyd(Graph& G, Matrix& d) {//O(V^3)
	d.resize(G.size());
	REP(i, d.size())d[i].resize(G.size());
	REP(i, d.size()) {
		REP(j, d[i].size()) {
			d[i][j] = INF;
		}
	}
	REP(i, G.size()) {
		REP(j, G[i].size()) {
			d[i][G[i][j].to] = G[i][j].cap;
		}
	}
	REP(i, G.size()) {
		REP(j, G.size()) {
			REP(k, G.size()) {
				chmin(d[j][k], d[j][i] + d[i][k]);
			}
		}
	}
}

class UnionFind {
	vector<int> data;
	int num;
public:
	UnionFind(int size) : data(size, -1), num(size) { }
	bool unionSet(int x, int y) {
		x = root(x); y = root(y);
		if (x != y) {
			if (data[y] < data[x]) swap(x, y);
			data[x] += data[y]; data[y] = x;
			num--;
		}
		return x != y;
	}
	bool findSet(int x, int y) {
		return root(x) == root(y);
	}
	int root(int x) {
		return data[x] < 0 ? x : data[x] = root(data[x]);
	}
	int size(int x) {
		return -data[root(x)];
	}
	int numSet() {
		return num;
	}
};

//nCr,nPr,modの逆元
class Combination {
public:
	Array fact;//n！
	Array inv;//n!の逆元
	ll mod;

	//modの逆元
	ll mod_inv(ll x) {
		ll n = mod - 2;
		ll res = 1LL;
		while (n > 0) {
			if (n & 1) res = res * x % mod;
			x = x * x % mod;
			n >>= 1;
		}
		return res;
	}
	ll nCr(ll n, ll r) {
		return ((fact[n] * inv[r] % mod) * inv[n - r]) % mod;
	}
	ll nPr(ll n, ll r) {
		return (fact[n] * inv[n - r]) % mod;
	}
	Combination(ll n, ll _mod) {
		mod = _mod;
		fact.resize(n + 1);
		fact[0] = 1;
		REP(i, n) {
			fact[i + 1] = (fact[i] * (i + 1LL)) % mod;
		}
		inv.resize(n + 1);
		REP(i, n + 1) {
			inv[i] = mod_inv(fact[i]);
		}
	}
};

//約数
void divisor(ll n, vector<ll>& ret) {
	for (ll i = 1; i * i <= n; i++) {
		if (n % i == 0) {
			ret.push_back(i);
			if (i * i != n) ret.push_back(n / i);
		}
	}
	sort(ret.begin(), ret.end());
}

//最大公約数
ll gcd(ll m, ll n) {
	if (n == 0)return m;
	return gcd(n, m % n);
}//gcd

//最小公倍数
ll lcm(ll m, ll n) {
	return m / gcd(m, n) * n;
}

//繰り返し自乗法
ll pow2(ll x, ll n) { //x^n 計算量O(logn)
	ll ans = 1ll;
	while (n > 0) {
		if ((n & 1) == 1) {
			ans = ans * x%MOD;
		}
		x = x * x%MOD; //一周する度にx, x^2, x^4, x^8となる
		n >>= 1; //桁をずらす n = n >> 1
	}
	return ans;
}

class MedSet {
public:
	multiset<ll> left, right;
	ll med;//中央値または中央値の左側
	MedSet() {}
	MedSet(ll _med) {

	}
	void insert(ll a) {
		if (left.size() == 0) {
			med = a;
			left.insert(med);
		}
		else {
			if (a < med) {
				left.insert(a);
				if (left.size() > right.size() + 1) {
					//left->right
					right.insert(*(--left.end()));
					left.erase(--left.end());
				}
				med = *(--left.end());
			}
			else {
				right.insert(a);
				if (right.size() > left.size()) {
					//right->left
					left.insert(*(right.begin()));
					right.erase(right.begin());
				}
				med = *(--left.end());
			}
		}
	}
};

//input
ll  N, M, L, K, A, B, C, D, Q, X;

int main()
{
	cin >> N >> K;
	if (N == 2) {
		cout << -1 << endl;
		return 0;
	}

	if (K>(N-1)*(N-2)/2) {
		cout << -1 << endl;
		return 0;
	}

	vector<P> v;

	ll n = sqrt(2*K)+1;

	if (K == 0) {
		cout <<0<< endl;
		return 0;
	}

	
	if (n>=N){
		cout << -1 << endl;
		return 0;
	}
	//cout << n << endl;
	REP(i, n) {
		v.push_back(make_pair(1, i + 2));
	}

	ll sum = n * (n - 1) / 2;
	ll x = N - (n+1);//残りの頂点数
	ll j = n + 1;
	while (sum!=K) {
		v.push_back(make_pair(j, j + 1));
		
		if (x == 0) {
			v.push_back(make_pair(n, j + 1));
		}

		sum++;
		x--;

		if (x < 0) {
			cout << -1 << endl;
			return 0;
		}
	}

	cout << v.size() << endl;
	for (auto i : v) {
		cout << i.first << " " << i.second << endl;
	}


	return 0;
}