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: Accepted)

# -*- coding: utf-8 -*-
"""
Created on Sun Jun 23 09:58:43 2019

@author: Yamazaki Kenichi
"""
import sys

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

max_n = ((N - 1) * (N - 2)) // 2

if K > max_n:
    ans = -1
    print(ans)
    sys.exit()

uv = []
for i in range(1,N):
    uv.append([N,i])

link_n = max_n - K
counta = 0
for i in range(1,N):
    for j in range(i+1,N):
        if counta == link_n:
            break
        uv.append([i,j])
        counta += 1
    else:
        continue
    break

M = N - 1 + link_n
print(M)
for c in uv:
    print(c[0],c[1])