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 (3.4.3) (judge verdict: Wrong Answer)

n,k = map(int,input().split())
s= n
ans=[]
freeNode = [2]
cur=2
ans.append([1,2])
if n==2 :
    if k>0:
        print(-1)
    else:
        print(1)
        print(1, 2)
        exit()
else:
    s=0
    c=1
    if (n-2)*(n-1)//2<k:
        print(-1)
        exit()
    else:
        while(1):
            s = c+1+s
            cur+=1
            freeNode.append(cur)
            ans.append([1,cur])
            if s >k:
                break
    if cur!=n:
        remove = len(ans)-k;
        if remove:
            for v in freeNode:
                ans.append([v,cur])
                remove-=1
                if remove==0:
                    break
        else:
            for i in range(cur+1,n+1):
                for j in range(1,cur+1):
                    ans.append([i,j])
        print(len(ans))
        for u,v in ans:
            print(u,v)