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 LuaJIT (2.0.4) (judge verdict: Wrong Answer)

local mfl, mce = math.floor, math.ceil
local mmi, mma = math.min, math.max
local bls, brs = bit.lshift, bit.rshift
local SegTree = {}
SegTree.updateAll = function(self)
  for i = self.stagenum - 1, 1, -1 do
    local cnt = bls(1, i - 1)
    for j = 1, cnt do
      self.stage[i][j] = self.func(self.stage[i + 1][j * 2 - 1], self.stage[i + 1][j * 2])
    end
  end
end
SegTree.create = function(self, n, func, emptyvalue)
  self.func, self.emptyvalue = func, emptyvalue
  local stagenum, mul = 1, 1
  self.stage = {{}}
  while mul < n do
    mul, stagenum = mul * 2, stagenum + 1
    self.stage[stagenum] = {}
  end
  self.stagenum = stagenum
  self.left_stage = {}
  for i = 1, n do
    local sp, sz = 1, bls(1, stagenum - 1)
    while(i - 1) % sz ~= 0 do
      sp, sz = sp + 1, brs(sz, 1)
    end
    self.left_stage[i] = sp
  end
  self.sz_stage = {}
  local tmp, sp = 1, stagenum
  for i = 1, n do
    if tmp * 2 == i then tmp, sp = tmp * 2, sp - 1 end
    self.sz_stage[i] = sp
  end
  for i = 1, n do self.stage[stagenum][i] = i end
  for i = n + 1, mul do self.stage[stagenum][i] = emptyvalue end
  self:updateAll()
end
SegTree.getRange = function(self, left, right)
  if left == right then return self.stage[self.stagenum][left] end
  local stagenum = self.stagenum
  local ret = self.emptyvalue
  while left <= right do
    local stage = mma(self.left_stage[left], self.sz_stage[right - left + 1])
    local sz = bls(1, stagenum - stage)
    ret = self.func(ret, self.stage[stage][1 + brs(left - 1, stagenum - stage)])
    left = left + sz
  end
  return ret
end
SegTree.update = function(self, idx, value)
  for i = self.stagenum - 1, 1, -1 do
    local dst = brs(idx + 1, 1)
    local rem = dst * 4 - 1 - idx
    self.stage[i][dst] = self.func(self.stage[i + 1][idx], self.stage[i + 1][rem])
    idx = dst
  end
end
SegTree.new = function(n, func, emptyvalue)
  local obj = {}
  setmetatable(obj, {__index = SegTree})
  obj:create(n, func, emptyvalue)
  return obj
end

local n, m = io.read("*n", "*n")
local edge = {}
local edgenum = {}
local offset = {}
for i = 1, n do
  edge[i] = {}
  edgenum[i] = 0
  offset[i] = 0
end
local inf = 1000000007
edgenum[n + 1] = inf
for i = 1, m do
  local a, b = io.read("*n", "*n")
  edge[a][b], edge[b][a] = true, true
  edgenum[a] = edgenum[a] + 1
  edgenum[b] = edgenum[b] + 1
end
if m % 2 == 1 then
  print(-1)
  os.exit()
end
local st = SegTree.new(n, function(a, b) return edgenum[a] < edgenum[b] and a or b end, n + 1)
for i = 1, n do
  local src = st.stage[1][1]
  local dsts = {}
  for dst, _u in pairs(edge[src]) do
    table.insert(dsts, dst)
  end
  local lim = mfl(#dsts / 2)
  for j = 1, lim * 2 do
    local dst = dsts[j]
    print(src .. " " .. dst)
    edge[dst][src] = nil
    edgenum[dst] = edgenum[dst] - 1
    st:update(dst)
  end
  if #dsts % 2 == 1 then
    local dst = dsts[#dsts]
    if offset[src] == 0 then
      print(dst .. " " .. src)
      offset[dst] = (offset[dst] + 1) % 2
    else
      print(src .. " " .. dst)
    end
    edge[dst][src] = nil
    edgenum[dst] = edgenum[dst] - 1
    st:update(dst)
  end
  edgenum[src] = inf
  st:update(src)
end