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)

import sys

N, K = map(int, input().split())

if N == 2:
    if K == 0:
        print("1")
        print("1 2")
        sys.exit()
    else:
        print("-1")
        sys.exit()

if K > (N-1)*(N-2)/2:
    print("-1")
    sys.exit()

k_list = []
val = 0
for i in reversed(range(2, N)):
    k_list.append(int(i*(i-1)/2+val))
    val += 1

if K not in k_list:
    print("-1")
    sys.exit()

print(N)
num = N-1 - k_list.index(K)
for i in range(1, num):
    print("1 {}".format(i+1))

val = 2
for i in range(num+1,N+1):
    print("{} {}".format(val, i))
    val = i