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

N,M=map(int,input().split())
EDGE=[list(map(int,input().split())) for i in range(M)]

if M%2!=0:
    print(-1)
    sys.exit()

E=[set() for i in range(N+1)]

for x,y in EDGE:
    E[x].add(y)
    E[y].add(x)

ECOUNT=[0]*(N+1)

from collections import deque


E_tree = [set() for i in range(N+1)]

Q=deque()
Q.append(1)
check=[0]*(N+1)
check[1]=1

TOP=[]
while Q:
    x=Q.pop()
    TOP.append(x)
    for to in E[x]:
        if check[to]==0:
            Q.append(to)
            E_tree[x].add(to)
            E_tree[to].add(x)
            check[to]=1

ECOUNT=[0]*(N+1)
for x,y in EDGE:
    if x in E_tree[y]:
        continue
    print(x,y)
    ECOUNT[x]+=1

#print(TOP[::-1])

for p in TOP[::-1][:-1]:
    q=list(E_tree[p])[0]

    if ECOUNT[p]%2==0:
        print(q,p)
        ECOUNT[q]+=1
    else:
        print(p,q)
    E_tree[q].remove(p)