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())


G = dict()
edge_dict = dict()
count_list = [0] * (N + 1)

for i in range(1, N + 1):
    G[i] = dict()
    edge_dict[i] = dict()

for _ in range(M):
    A, B = map(int, input().split())
    if A > B:
        A, B = B, A
    G[A][B] = 1
    G[B][A] = 1
    edge_dict[A][B] = 1
    edge_dict[B][A] = -1
    count_list[A] += 1

if M % 2 == 1:
    print(-1)
else:
    # minimum spanning tree
    parent = [0] * (N + 1)
    node_list = []
    queue = deque([1])
    visited = [0] * (N + 1)
    # BFS
    while len(queue) > 0:
        p = queue.popleft()
        for q in G[p].keys():
            if visited[q]:
                continue
            else:
                parent[q] = p
                visited[q] = 1
                queue.append(q)
                node_list.append(q)

    while len(node_list) > 0:
        q = node_list.pop()
        p = parent[q]
        if count_list[q] % 2 == 1:
            edge_dict[p][q] *= -1
            edge_dict[q][p] *= -1
            count_list[p] += 1
            count_list[q] += 1

    for i in range(1, N + 1):
        for j in edge_dict[i].keys():
            if edge_dict[i][j] == 1:
                print(i, j)