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())

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

graph = [[] for _ in range(N)]
for _ in range(M):
    u, v = map(int, input().split())
    graph[u - 1].append(v - 1)
    graph[v - 1].append(u - 1)

ans = []
parent = [-1] * N
visited = [False] * N
ctr = [0] * N
record = []
que = [(-1, 0)]

while que:
    pre, u = que.pop()
    if visited[u]:
        ctr[u] += 1
        if pre >= 0:
            ans.append((u, pre))
        continue
        
    visited[u] = True
    record.append(u)
    for v in graph[u]:
        if v != parent[u]:
            parent[v] = u
            graph[v].remove(u)
            que.append((u, v))
            
for u in record[1:][::-1]:
    if ctr[u] % 2 == 1:
        ans.append((u, parent[u]))
    else:
        ans.append((parent[u], u))
        ctr[parent[u]] += 1
        
for x, y in ans:
    print(x + 1, y + 1)