Problem: 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.

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.

Examples

Input

4 4
1 2
2 3
3 4
4 1


Output

1 2
1 4
3 2
3 4


Input

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


Output

-1

Solution (in PYTHON3):

Solution:
import sys
# input = sys.stdin.readline
sys.setrecursionlimit(pow(10, 6))

n, m = map(int, input().split())
graph = [[] for _ in range(n)]
dgraph = [[] for _ in range(n)]
edges = [[] for _ in range(n)]
eds = set()
visited = [False for i in range(n)]

def spanning_tree(i):
  if visited[i]:
    return
  visited[i] = True
  for to in graph[i]:
    if not visited[to]:
      edges[i].append(to)
      eds.add((i, to))
      spanning_tree(to)

def const_dgraph(i):
  ce = 0
  for to in edges[i]:
    c = const_dgraph(to)
    if c == 0:
      dgraph[i].append(to)
    else:
      dgraph[to].append(i)
  return len(dgraph[i]) % 2

if m % 2 == 1:
  print(-1)
else:
  for _ in range(m):
    a, b = map(int, input().split())
    graph[a-1].append(b-1)
    graph[b-1].append(a-1)
  spanning_tree(0)
  for i, g in enumerate(graph):
    for to in g:
      if (i, to) not in eds and (to, i) not in eds:
        dgraph[i].append(to)
        eds.add((i, to))
  visited = [False for _ in range(n)]
  const_dgraph(0)
  if len(dgraph[0]) % 2 == 1:
    print(-1)
  else:
    for i, g in enumerate(dgraph):
      for to in g:
        print("%d %d" % (i+1, to+1))