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,collections
sys.setrecursionlimit(10**7)
n,m = map(int,input().split())
vertices_in = [set() for _ in range(n+1)]
vertices_out = [set() for _ in range(n+1)]
nodes= [1]*(n+1)
done = set()
use = set()
dq = collections.deque([])
for i in range(m):
    a,b=map(int,sys.stdin.readline().split())
    vertices_in[a].add(b)
    vertices_in[b].add(a)
dq.append(1)
order = [1]
def factory(num):
    for v in vertices_in[num]:
        if v not in done:
            done.add(v)
            factory(v)
    for v in vertices_in[num]:
        if num not in vertices_out[v]:
            vertices_out[num].add(v)
            use.add(v)
    if len(vertices_out[num])%2!=0:
        for v in vertices_out[num]:
            if nodes[v]:
                vertices_out[num].remove(v)
                use.remove(v)
                break
    nodes[num]=0
if m%2==1:
    print(-1)
else:
    factory(1)
    for i in range(1,n+1):
        for v in vertices_out[i]:
            print(i,v)