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 PyPy3 (7.3.0) (judge verdict: Accepted)

from itertools import combinations
from collections import deque
n,k = map(int,input().split())
i_canerase = [n-2] * n
import sys
q = deque(combinations([i for i in range(n)],2))
use_edges = []
canmake = 0
while q:
    if canmake == k:
        use_edges += list(q)
        print(len(use_edges))
        for i in range(len(use_edges)):
            a,b = use_edges[i]
            print(a+1,b+1)
        sys.exit()

    a,b = q.popleft()
    if i_canerase[a]>0 and i_canerase[b]>0:
        i_canerase[a] -= 1
        i_canerase[b] -= 1
        canmake += 1
    else:
        use_edges.append([a,b])

print(-1)