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 Pascal (FPC 2.6.2) (judge verdict: Accepted)

var
	N,K,i,u,v:Longint;
	S:String;
procedure f(u:Longint);
begin
	if u=100 then S:=S+'100'
	else begin
		if u>9 then S:=S+chr(u div 10+48);
		S:=S+chr(u mod 10+48);
	end;
end;
begin
	read(N,K);
	if (N-1)*(N-2)<K*2 then begin
		writeln(-1);
		exit;
	end;
	K:=(N-1)*(N-2)div 2-K;
	writeln(K+N-1);
	for i:=2 to N do begin
		S:=S+'1 ';
		f(i);
		S:=S+' ';
	end;
	for u:=2 to N do begin
		if K=0 then break;
		for v:=u+1 to N do begin
			if K=0 then break;
			f(u);
			S:=S+' ';
			f(v);
			S:=S+' ';
			dec(K);
		end;
	end;
	writeln(S);
end.