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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)


import java.util.*;
import java.io.*;

class Main{
    public static void main(String[] args){
        FastScanner fs = new FastScanner();
        int n =fs.nextInt();
        int k = fs.nextInt();
        if(k > (n-1)*(n-2)/2){
            System.out.println(-1);
        }else{
            List<List<Integer>> res = new ArrayList<>();
            for(int i=0;i<n;i++){
                res.add(new LinkedList<>());
            }
            for(int i=1;i<n;i++){
                res.get(0).add(i);
            }
            int require = (n-1)*(n-2)/2-k;
            int cnt = 0;
            for(int i=1;i<n-1 && cnt < require;i++){
                for(int j=i+1;j<n && cnt < require;j++){
                    res.get(i).add(j);
                    cnt++;
                }
            }
            PrintWriter out = new PrintWriter(System.out);
            out.println(n-1+require);
            for(int i=0;i<n;i++){
                for(Integer to : res.get(i)){
                    out.print(i+1);
                    out.print(' ');
                    out.println(to+1);
                }
            }
            out.flush();
            
        }
    }
    static class FastScanner{
        private final InputStream in = System.in;
        private final byte[] buffer = new byte[1024];
        private int ptr = 0;
        private int buflen = 0;

        private boolean hasNextByte(){
            if(ptr < buflen){
                return true;
            }else{
                ptr = 0;
                try{
                    buflen = in.read(buffer);
                }catch(IOException e){
                    e.printStackTrace();
                }
                if(buflen <= 0){
                    return false;
                }
            }
            return true;
        }

        private int readByte(){
            if(hasNextByte())return buffer[ptr++];
            else return -1;
        }

        private boolean isPrintableChar(int c){
            return 33<=c && c<=126;
        }

        public boolean hasNext(){
            while(hasNextByte() && !isPrintableChar(buffer[ptr]))ptr++;
            return hasNextByte();
        }

        public String next(){
            if(!hasNext()) throw new NoSuchElementException();
            StringBuilder sb = new StringBuilder();
            int b = readByte();
            while(isPrintableChar(b)){
                sb.appendCodePoint(b);
                b = readByte();
            }
            return sb.toString();
        }

        public long nextLong(){
            if(!hasNext()) throw new NoSuchElementException();
            long n = 0;
            boolean minus = false;
            int b = readByte();
            if(b == '-'){
                minus = true;
                b = readByte();
            }
            if(b < '0' || '9' < b){
                throw new NumberFormatException();
            }
            while(true){
                if('0' <= b && b<='9'){
                    n*=10;
                    n+=b-'0';
                }else if(b==-1 || !isPrintableChar(b)){
                    return minus ? -n : n;
                }else{
                    throw new NumberFormatException();
                }
                b = readByte();
            }
        }
        public int nextInt(){
            long nl = nextLong();
            if(nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE)throw new NumberFormatException();
            return (int)nl;
        }
        public double nextDouble(){return Double.parseDouble(next());}
    }
}