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)

def check(N, K):
    if K < N - 2:
        print(-1)
        return
    if N-2 <= K and K <= (N - 1)*(N-2) /2:
        k = int((N - 1)*(N-2) /2 - K)
        print(N-1 + k)
        for i in range(2, N+1):
            print(1, i)
        l = 2
        r = 3
        for i in range(k):
            print(l, r)
            r+=1
            if r == N+1:
                l+=1
                r=l+1
        return
    if (N - 1)*(N - 2) /2 < K:
        print(-1)
        return


if __name__ == "__main__":
    N, K = map(int, input().split())
    check(N, K)