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.io.*;
import java.math.*;
import java.security.KeyStore.Entry;
import java.util.*;

public class Main {
	private static boolean[] vis;
	private static long[] dist;
	private static long mod = 1000000000 + 7;
	public static void merge(int arr[], int l, int m, int r) 
    { 
        // Find sizes of two subarrays to be merged 
        int n1 = m - l + 1; 
        int n2 = r - m; 
  
        /* Create temp arrays */
        int L[] = new int [n1]; 
        int R[] = new int [n2]; 
  
        /*Copy data to temp arrays*/
        for (int i=0; i<n1; ++i) 
            L[i] = arr[l + i]; 
        for (int j=0; j<n2; ++j) 
            R[j] = arr[m + 1+ j]; 
  
  
        /* Merge the temp arrays */
  
        // Initial indexes of first and second subarrays 
        int i = 0, j = 0; 
  
        // Initial index of merged subarry array 
        int k = l; 
        while (i < n1 && j < n2) 
        { 
            if (L[i] <= R[j]) 
            { 
                arr[k] = L[i]; 
                i++; 
            } 
            else
            { 
                arr[k] = R[j]; 
                j++; 
            } 
            k++; 
        } 
  
        /* Copy remaining elements of L[] if any */
        while (i < n1) 
        { 
            arr[k] = L[i]; 
            i++; 
            k++; 
        } 
  
        /* Copy remaining elements of R[] if any */
        while (j < n2) 
        { 
            arr[k] = R[j]; 
            j++; 
            k++; 
        } 
    } 
	 public static void sort(int arr[], int l, int r) 
	    { 
	        if (l < r) 
	        { 
	            // Find the middle point 
	            int m = (l+r)/2; 
	  
	            // Sort first and second halves 
	            sort(arr, l, m); 
	            sort(arr , m+1, r); 
	  
	            // Merge the sorted halves 
	            merge(arr, l, m, r); 
	        } 
	    } 
	 private static long gcd(long n, long l) {
	        if (l == 0)
	            return n;
	        return gcd(l, n % l);
	    }
	 private static int gcd(int n, int l) {
	        if (l == 0)
	            return n;
	        return gcd(l, n % l);
	    }
	 public static void dfs(ArrayList<Integer>[] gr,int v)
	    {
	         vis[v]=true;
	         ArrayList<Integer> arr=gr[v];
	         for(int i=0;i<arr.size();i++)
	         {
	             if(!vis[arr.get(i)])
	             {  
	            	 
	            	 dfs(gr,arr.get(i));
	             }
	         }
	    }
	 private static class Pairs implements Comparable<Pairs>{
	        String v;int i;int j;
	        public Pairs(String a,int b,int c){
	            v=a;
	            i=b;
	            j=c;
	        }
	        @Override
	        public int compareTo(Pairs arg0) {
	            {
	            	if(!this.v.equals(arg0.v))
	            		return this.v.compareTo(arg0.v);
	            	else
	            		return arg0.i-this.i;
	            }
	        }
	    }
	 private static class Pair implements Comparable<Pair>{
	        int v,i;Pair j;
	        public Pair(int a,int b){
	            v=a;
	            i=b;
	        }
	        public Pair(int a,Pair b)
	        {
	            v=a;
	            j=b;
	        }
	        @Override
	        public int compareTo(Pair arg0) {
	            {
	            	if(this.i!=arg0.i)
	            		return this.i-arg0.i;
	            	else
	            		return arg0.v-this.v;
	            }
	        }
	    }
	 public static long mmi(long a, long m) 
	    { 
	        long m0 = m; 
	        long y = 0, x = 1; 
	      
	        if (m == 1) 
	          return 0; 
	      
	        while (a > 1) 
	        { 
	            // q is quotient 
	            long q = a / m; 
	            long t = m; 
	      
	            // m is remainder now, process same as 
	            // Euclid's algo 
	            m = a % m; a = t; 
	            t = y; 
	      
	            // Update y and x 
	            y = x - q * y; 
	            x = t; 
	        } 
	      
	        // Make x positive 
	        if (x < 0) 
	           x += m0; 
	      
	        return x; 
	    }
	private static long pow(long a, long b, long c) {
	        if (b == 0)
	            return 1;
	        long p = pow(a, b / 2, c);
	        p = (p * p) % c;
	        return (b % 2 == 0) ? p : (a * p) % c;
	    }
	public static int ub(ArrayList<Integer> array, int low,int high, int value) {
        while (low < high) {
            final int mid = (low + high) / 2;
            if (value >= array.get(mid)) {
                low = mid + 1;
            } else {
                high = mid;
            }
        }
        return low;
	}
	public static void main(String[] args) throws Exception
	{
		Scanner sc=new Scanner(System.in);
		int n=sc.nextInt();
		int k=sc.nextInt();
		ArrayList<Pair> arr=new ArrayList<>();
		for(int i=2;i<=n;i++)
			arr.add(new Pair(1,i));
		int max=((n-1)*(n-2))/2;
		int diff=max-k;
		if(diff==0)
		{
			System.out.println(arr.size());
			for(int i=0;i<arr.size();i++)
				System.out.println(arr.get(i).v+" "+arr.get(i).i);
			return;
		}
		for(int i=2;i<=n;i++)
		{
			for(int j=i+1;j<=n;j++)
			{
				arr.add(new Pair(i,j));
				diff--;
				if(diff==0)
					break;
			}
			if(diff==0)
				break;
		}
		if(diff==0)
		{
			System.out.println(arr.size());
			for(int i=0;i<arr.size();i++)
				System.out.println(arr.get(i).v+" "+arr.get(i).i);
		}
		else
			System.out.println("-1");
	}
}