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 PyPy3 (2.4.0) (judge verdict: Wrong Answer)

n,k = map(int, input().split())

graph = [[] for i in range(n)]
if k > (n-1)*(n-2)//2:
    print(-1)
else:
    for i in range(1,n):
        graph[0].append(i+1)
    
    remain = (n-1)*(n-2)//2 - k
    for i in range(1,n):
        if remain <= 0:
            break
        for j in range(i+1,n):
            remain -= 1
            if remain > 0:
                graph[i].append(j+1)
            else:
                break


    for i in range(len(graph)):
        for j in range(len(graph[i])):
            print(i+1, graph[i][j])