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 Python (3.8.2) (judge verdict: Wrong Answer)

n,k = map(int,input().split())
res_graph = [[1,i] for i in range(2,n+1)]
res = (n-1)*(n-2)//2

if(k > (n-2)*(n-1)//2):
    print(-1)
    exit()

tmp = 1
tmp_edge = 2
while 1:
    chek = [0]*(n-tmp_edge)
    for i in range(tmp_edge-1,len(chek)+1):
        res_graph.append([tmp_edge, i+tmp_edge])
        res -=1
        if(res==k):
            break
    tmp_edge+=1
    if res==k:
        break
    if tmp_edge == n:
        print(-1)
        exit()
print(len(res_graph))
for i,j in res_graph:
    print(i,j)