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>

using namespace std;

#define rep(i, n) for (int i = 0; i < (n); ++i)
#define eee(a) (cerr << (#a) << ": " << (a) << endl);


using ll = long long;
using pint = pair<int, int>;
using pll = pair<ll, ll>;
using mint = map<int, int>;

int dx[4] = {1, 0, -1, 0};
int dy[4] = {0, 1, 0, -1};

const char sp = ' ';
const char cmm = ',';
const int MOD = 1e9+7;
const int INF = 1e9;
const ll LINF = 1e18;

ll mod(ll a, ll b){return (a%b+b)%b;}
ll gcd(ll a, ll b){return b?gcd(b,a%b):a;}
ll lcm(ll a, ll b){return a*b/gcd(a,b);}
void Yes(){cout << "Yes" << endl;}
void No(){cout << "No" << endl;}
void Judge(bool b){b?Yes():No();}
void YES(){cout << "YES" << endl;}
void NO(){cout << "NO" << endl;}
void JUDGE(bool b){b?YES():NO();}
ll powmod(ll b, ll e){ll r=1;while(e>0){if(e&1)r=(r%MOD)*(b%MOD)%MOD;b=(b%MOD)*(b%MOD)%MOD;e>>=1;}return r;}
double distance(ll x1, ll y1, ll x2, ll y2){return sqrt((x1-x2)*(x1-x2) + (y1-y2)*(y1-y2));}

template<class T>bool chmax(T &a, const T &b) { if (a<b) { a=b; return 1; } return 0; }
template<class T>bool chmin(T &a, const T &b) { if (b<a) { a=b; return 1; } return 0; }
template<typename T>
void ppp(T n){cout << n << endl;}
template<typename T1, typename T2> ostream& operator<<(ostream& s, const pair<T1, T2>& p) {return s << "(" << p.first << ", " << p.second << ")";}
template<typename T> ostream& operator<<(ostream& s, const vector<T>& v) {
    int len = v.size();
    s << '[';
    for (int i = 0; i < len; ++i) {
        s << v[i]; if (i < len-1) s << ", ";
    }
    s << ']';
    return s;
}

struct aaa{
    aaa(){
        cin.tie(0); ios::sync_with_stdio(0); cout<<fixed<<setprecision(15);
    };
}fastio;

int main(){

    ll n, k;
    cin >> n >> k;
    if(k > n-2){
        ppp(-1);
        return 0;
    }
    if(k == 0){
        cout << n*(n-1)/2 << endl;
        for(int i = 1; i <= n; ++i){
            for(int j = i+1; j <= n; ++j){
                printf("%d %d\n", i, j);
            }
        }
        return 0;
    }
    
    ll m = (k+2)*(n-k-2)+k+1;
    if(n-k-2 >= 1) m += n-k-3;
    cout << m << endl;
    for(int i = 1; i <= k+1; ++i){
        cout << i << sp << i+1 << '\n';
    }
    // cout << "OK1" << endl;
    for(int i = k+3; i <= n; ++i){
        for(int j = 1; j <= k+2; ++j){
            int a = min(i, j), b = max(i, j);
            printf("%d %d\n", a, b);
        }
    }
    // cout << "OK2" << endl;
    for(int i = k+3; i+1 <= n; ++i){
        printf("%d %d\n", i, i+1);
    }
    // cout << "OK3" << endl;



    return 0;
}