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 Fortran (gfortran v4.8.4) (judge verdict: Wrong Answer)

integer N,K
integer cnt
read*,N,K
if(K>(N-1)*(N-2)/2)then
  print"(i0)",-1
  stop
endif

print"(i0)",(N-1) +((N-1)*(N-2)/2 - K)
do i=1,n-1
  print"(i0,A,i0)",i," ",N
end do

cnt=0
do i=1,n-2
  do j=i+1,n-1
    print"(i0,A,i0)",i," ",j
    cnt=cnt+1
    if( cnt==(N-1)*(N-2)/2 -K )then
      stop
    end if
  end do
end do
end