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(10**7)

n, m = map(int, input().split())
if m%2:
  print(-1)
else:
  G = [[] for _ in range(n+1)]
  par = [-1]*(n+1)
  ch = [[] for _ in range(n+1)]
  seen = [False]*(n+1)
  used = set()
  C = [0]*(n+1)
  for _ in range(m):
    a, b = map(int, input().split())
    G[a].append(b)
    G[b].append(a)
  
  stack = [1]
  seen[1] = True
  while stack:
    v = stack.pop()
    for nv in G[v]:
      if seen[nv]:
        if par[v] != nv:
          if (min(v, nv), max(v, nv)) not in used:
            used.add((min(v, nv), max(v, nv)))
            print(v, nv)
            C[v] ^= 1
      else:
        seen[nv] = True
        par[nv] = v
        ch[v].append(nv)
        stack.append(nv)
  
  def bottom_up(v):
    for nv in ch[v]:
      bottom_up(nv)
    if v == 1:
      return
    if C[v]:
      C[v] ^= 1
      print(v, par[v])
    else:
      C[par[v]] ^= 1
      print(par[v], v)
      
  bottom_up(1)