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
N, M = map(int, input().split())
V = {i: [] for i in range(1,N+1)}
for _ in range(M):
    a, b = map(int, input().split())
    V[a].append(b)
    V[b].append(a)

def zen(V):
    W = []
    q = deque()
    q.append(1)
    vstd = {i: 0 for i in range(1,N+1)}

    while q:
        u = q.popleft()
        if vstd[u]:
            continue
        vstd[u] = True
        W.append(u)
        for v in V[u]:
            if vstd[v]:
                continue
            q.append(v)
    return W

if M % 2 != 0:
    print(-1)
else:

    U = zen(V)
    W = {i: [] for i in range(1,N+1)}

    for u in U[::-1]:
        for v in V[u]:
            if v in W[u] or u in W[v]:
                continue
            if len(W[u]) % 2 == 0:
                W[v].append(u)
            else:
                W[u].append(v)

    for w in W:
        for v in W[w]:
            print(w, v)