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 deque
class UnionFind():
    n=1
    par=[0]
    rnk=[0]
    def __init__(self,size):
        self.n=size
        self.par=[i for i in range(self.n)]
        self.rnk=[0 for i in range(self.n)]
    def find(self,vertex1):
        if self.par[vertex1]==vertex1:
            return vertex1
        else:
            self.par[vertex1]=self.find(self.par[vertex1])
            return self.par[vertex1]
    def unite(self,vertex1,vertex2):
        vertex1=self.find(vertex1)
        vertex2=self.find(vertex2)
        if vertex1==vertex2:
            return
        if (self.rnk[vertex1]<self.rnk[vertex2]):
            self.par[vertex1]=vertex2
        else:
            self.par[vertex2]=vertex1
            if(self.rnk[vertex1]==self.rnk[vertex2]):
                self.rnk[vertex1]+=1
    def same(self,vetrex1,vertex2):
        return self.find(vetrex1)==self.find(vertex2)

N,M=map(int,input().split())
if M%2==1:
    print(-1)
    exit()
edges=[]
tree=[]
G=UnionFind(N)
H=[[] for i in range(N)]
T=[[] for i in range(N)]
for i in range(M):
    a,b=map(int,input().split())
    a-=1;b-=1
    if G.same(a,b):
        edges.append((a,b))
        H[a].append(b)
    else:
        tree.append((a,b))
        G.unite(a,b)
        T[a].append(b)
        T[b].append(a)
#print(edges)
#print(tree)
q=deque([0])
reached=[0 for i in range(N)]
search=deque([])
parents=[-1 for i in range(N)]
while(len(q)>0):
    #print(q,reached,search)
    r=q.popleft()
    reached[r]=1
    for p in T[r]:
        if reached[p]==0:
            q.append(p)
            parents[p]=r
            search.appendleft(p)
#print(parents)
for i in range(N-1):
    v=search.popleft()
    p=parents[v]
    if len(H[v])%2==0:
        H[p].append(v)
    else:
        H[v].append(p)
for i in range(N):
    for j in H[i]:
        print(i+1,j+1)