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:
from collections import defaultdict
import sys
sys.setrecursionlimit(1000000)
input = sys.stdin.readline

n, m = list(map(int, input().split()))

if m%2==1:
  print(-1)
  exit()

graph = defaultdict(set)
grapht = defaultdict(set)
for i in range(m):
  a, b = list(map(int, input().split()))
  a -= 1
  b -= 1
  graph[a].add(b)
  graph[b].add(a)
  grapht[a].add(b)
  grapht[b].add(a)

graph2 = defaultdict(set)
visited = [0 for i in range(n)]
num = [1 for i in range(n)]

def dfs(x):
  visited[x] = 1

  for nx in graph[x]:
    if not visited[nx]:
      dfs(nx)

  t = set()
  if num[x]==1 and len(grapht[x])%2==0:
    for e in grapht[x]:
      graph2[x].add(e)
      t.add(e)
  elif num[x]==-1 and len(grapht[x])%2==0:
    for j, e in enumerate(grapht[x]):
      if j==len(grapht[x])-1:
        graph2[e].add(x)
        num[e] *= -1
      else:
        graph2[x].add(e)
      t.add(e)
  elif num[x]==1 and len(grapht[x])%2==1:
    for j, e in enumerate(grapht[x]):
      if j==len(grapht[x])-1:
        graph2[e].add(x)
        num[e] *= -1
      else:
        graph2[x].add(e)
      t.add(e)
  elif num[x]==-1 and len(grapht[x])%2==1:
    for e in grapht[x]:
      graph2[x].add(e)
      t.add(e)
  for e in t:
    grapht[x].remove(e)
    grapht[e].remove(x)

dfs(0)

for i in range(n):
  for e in graph2[i]:
    print(i+1, e+1)