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:
n,m = map(int,input().split())

edges = []
parity = [0]*n
di = {}
C = [[] for _ in range(n)]
for _ in range(m):
    a,b = [int(x)-1 for x in input().split()]
    C[a].append(b)
    C[b].append(a)
    edges.append((a,b))
    parity[b] ^= 1
    di[a,b] = 0 # a <- b

if sum(parity)%2 == 1:
    print(-1)
else:
    parent = [-1]*n
    parent[0] = 0
    Q = [0]

    order = []
    for cur in Q:
        for neigh in C[cur]:
            if parent[neigh] == -1:
                order.append(neigh)
                parent[neigh] = cur
                Q.append(neigh)
    
    for v in reversed(order):
        if parity[v] == 1:
            u = v
            p = parent[u]
            if (u,p) not in di:
                u,p = p,u
            di[u,p] ^= 1
            parity[v] ^= 1
            parity[parent[v]] ^= 1
    for a,b in edges:
        if di[a,b] == 0:
            print(b+1,a+1)
        else:
            print(a+1,b+1)