Problem:
Score : 700 points

Problem Statement

You are given a simple connected undirected graph with N vertices and M edges. The vertices are numbered 1 to N, and the i-th edge connects Vertex A_i and Vertex B_i.
Takahashi will assign one of the two possible directions to each of the edges in the graph to make a directed graph.
Determine if it is possible to make a directed graph with an even number of edges going out from every vertex. If the answer is yes, construct one such graph.

Notes

An undirected graph is said to be simple when it contains no self-loops or multiple edges.

Constraints

2 \leq N \leq 10^5

N-1 \leq M \leq 10^5

1 \leq A_i,B_i \leq N (1\leq i\leq M)

The given graph is simple and connected.

Input

Input is given from Standard Input in the following format:

N M
A_1 B_1
:
A_M B_M

Output

If it is impossible to assign directions to satisfy the requirement, print -1.
Otherwise, print an assignment of directions that satisfies the requirement, in the following format:

C_1 D_1
:
C_M D_M

Here each pair (C_i, D_i) means that there is an edge directed from Vertex C_i to Vertex D_i. The edges may be printed in any order.

Sample Input 1

4 4
1 2
2 3
3 4
4 1

Sample Output 1

1 2
1 4
3 2
3 4

After this assignment of directions, Vertex 1 and 3 will each have two outgoing edges, and Vertex 2 and 4 will each have zero outgoing edges.

Sample Input 2

5 5
1 2
2 3
3 4
2 5
4 5

Sample Output 2

-1

Solution in Ruby (2.3.3) (judge verdict: Runtime Error)

n, m = gets.chomp.split(' ').map(&:to_i)
edges = []
1.upto(m) do
  edges << gets.chomp.split(' ').map(&:to_i)
end

# @return Array
def bit_strings(m)
  max_digit = m
  binary_numbers = (0..m**2-1).to_a.map{|m| m.to_s(2)}
  binary_numbers.map do |v|
    offset = max_digit - v.size
    "0" * offset + v
  end
end

# @return Bool
def check_edge(edges, n)
  vertex_cnt = Array.new(n).fill(0)
  edges.each do |e|
    vertex_cnt[e[0] - 1] += 1
  end
  vertex_cnt.count{|v| v.odd?} == 0
end

def convert(edges, b)
  new_edges = []
  b.split('').each_with_index do |v, i|
    if v == "0"
      new_edges[i] = edges[i]
    else
      new_edges[i] = [edges[i][1], edges[i][0]]
    end
  end
  new_edges
end

# @return false
# @return Array
def search(edges, bit_strings, n)
  bit_strings.each do |b|
    new_edges = convert(edges, b)
    return new_edges if check_edge(new_edges, n)
  end
  false
end

result = search(edges, bit_strings(m), n)
if result
  result.each_with_index do |r, i|
    print r[0].to_s + ' ' + r[1].to_s
    print "\n" if i != result.size-1
  end
else
  print -1
end