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:
import sys
input = sys.stdin.readline

N, M = map(int, input().split())
G = [set() for _ in range(N+1)]
for _ in range(M):
    A, B = map(int, input().split())
    G[A].add(B)
    G[B].add(A)
if M % 2 == 1:
    print(-1)
    exit()
G2 = [set() for _ in range(N+1)]
parent = [0] * (N+1)
depth = [-1] * (N+1)
depth[1] = 0
stack = [1]
while stack:
    v = stack.pop()
    if len(G[v]) > 0 and v != 1:
        depth[v] = depth[parent[v]] + 1
    for c in G[v]:
        G2[v].add(c)
        parent[c] = v
        if v in G[c]:
            G[c].remove(v)
        stack.append(c)
    G[v] = set()
nodes = sorted(list(range(1, N+1)), key=lambda v: -depth[v])
ans = []
for v in nodes:
    for c in G2[v]:
        ans.append((v, c))
    if len(G2[v]) % 2 == 1:
        p = parent[v]
        ans.append((v, p))
        G2[p].remove(v)
for u, v in ans:
    print(u, v)