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())

t = 10000
s, u = 0, 0
for k in range(1,10000):
    if K%k == 0:
        if t > k+K//k:
            t = k+K//k
            s, u = k, K//k

if t+1 > N:
    print(-1)
    exit(0)
else:
    ans = []
    print(s,u)
    a = [k+2 for k in range(s)]
    b = [k+1 for k in range(s+1,N)]
    for e in a:
        ans.append([1,e])
    for e in b:
        ans.append([1,e])

    for k in range(len(a)-1):
        for l in range(k+1,len(a)):
            ans.append([a[k],a[l]])
    for k in range(len(b)-1):
        for l in range(k+1,len(b)):
            ans.append([b[k],b[l]])
    print(len(ans))
    for e in ans:
        print(*e)