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 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include<stdio.h>

#define min(a,b) ((a)<(b)?(a):(b))

int main(){
	int n,k,i,j,g=-1;
	scanf("%d%d",&n,&k);
	for(i=0;i<n;i++){
		if(i*(n-i-1)+i*(i-1)/2>=k){
			g=i;
			break;
		}
	}
	if(g==-1){
		puts("-1");
		return 0;
	}
	int anss[10000][2],c=0;
	for(i=1;i<=n-g;i++){
		for(j=i+1;j<=n-g;j++){
			anss[c][0]=i;
			anss[c][1]=j;
			c++;
		}
	}
	for(i=n-g+1;i<=n;i++){
		anss[c][0]=i;
		anss[c][1]=1;
		c++;
	}
	int nok=g*(n-g-1)+g*(g-1)/2-k;
	int nn=nok;
	for(i=0;i<=nok/(n-g-1);i++){
		for(j=0;j<min(nn,(n-g-1));j++){
			anss[c][0]=j+2;
			anss[c][1]=n-g+1+j;
			c++;
		}
		nn-=(n-g-1);
		if(nn<=0)break;
	}
	printf("%d\n",c);
	for(i=0;i<c;i++)printf("%d %d\n",anss[i][0],anss[i][1]);
	return 0;
}