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
from collections import deque
n,m=map(int,input().split())
Edges=[[] for _ in range(n)]
for _ in range(m):
    a,b=map(int,input().split())
    a-=1; b-=1
    Edges[a].append(b)
    Edges[b].append(a)
if m%2:
    print(-1)
    exit()
Ans=[]
AnsSet=set()
Par=[-1]*n
V=[]
Visited=[False]*n
Cnt=[0]*n
q=deque([0])
Visited[0]=True
while q:
    fr=q.popleft()
    for to in Edges[fr]:
        if to==Par[fr] or (to,fr) in AnsSet:
            continue
        if Visited[to]:
            AnsSet.add((fr,to))
            Ans.append((fr,to))
            Cnt[fr]+=1
        else:
            Par[to]=fr
            Visited[to]=True
            q.append(to)
            V.append(to)
for v in V[::-1]:
    if Cnt[v]%2:
        Ans.append((v,Par[v]))
    else:
        Ans.append((Par[v],v))
        Cnt[Par[v]]+=1
for c,d in Ans:
    print(c+1,d+1)