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 = [int(i) for i in input().split()]

if N < K:
    print(-1)
    quit()

if N == 2:
    if K == 0:
        print(1)
        print(1, 2)
    else:
        print(-1)
    quit()

if N == 3:
    if K == 0:
        print(3)
        print(1, 2)
        print(2, 3)
        print(3, 1)
    elif K == 1:
        print(2)
        print(1, 2)
        print(2, 3)
    else:
        print(-1)
    quit()

if N == 4:
    if K == 0:
        print(6)
        print(1, 2)
        print(2, 3)
        print(3, 4)
        print(4, 1)
        print(1, 3)
        print(2, 4)
    elif K == 1:
        print(-1)
    elif K == 2:
        print(4)
        print(1, 2)
        print(2, 3)
        print(3, 4)
        print(4, 1)
    quit()


ans = []
for i in range(N - 1):
    ans.append((i + 1, i + 2))
ans.append((N, 1))

count = 0
u = 1
while count < N - K:
    ans.append((u, u + 2))
    count += 1
    if count >= N - K:
        break
    ans.append((u, u - 2 + N))
    count += 1
    u += 1

M = len(ans)
print(M)
for a in ans:
    print(*a)