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
sys.setrecursionlimit(10**6)
input = sys.stdin.readline

n, m = [int(item) for item in input().split()]
if m % 2 != 0:
    print(-1)
    exit()
visited_e = [False] * m
visited_v = [False] * n
edge = [[] for _ in range(n)]
for i in range(m):
    a, b = [int(item) for item in input().split()]
    a -= 1; b -= 1
    edge[a].append([b, i])
    edge[b].append([a, i])
 
ans = []
def dfs(prev, n):
    if visited_v[n]:
        return 1
    visited_v[n] = True
    child_num = 0
    for v, index in edge[n]:
        if visited_e[index]:
            continue
        visited_e[index] = True
        if dfs(n, v) == 1:
            child_num += 1
            ans.append([n+1, v+1])
    if child_num % 2 == 0:
        return 1
    else:
        ans.append([n+1, prev+1])
        return 0
 
dfs(-1, 0)
print("\n".join([str(f) + " " + str(t) for f, t in ans]))