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
sys.setrecursionlimit(10**6)

N,M = map(int,input().split())
if M&1:
    print(-1)
    exit()

AB = [[int(x) for x in input().split()] for _ in range(M)]

graph = [[] for _ in range(N+1)]
for a,b in AB:
    graph[a].append(b)
    graph[b].append(a)

# まずは全域木をつくる
tree = [set() for _ in range(N+1)]
visited = [False] * (N+1)
q = [1]
while q:
    x = q.pop()
    for y in graph[x]:
        if visited[y]:
            continue
        visited[y] = True
        tree[x].add(y)
        tree[y].add(x)
        q.append(y)

answer = []
out_deg = [0] * (N+1)
# 木を残して適当に決める
for a,b in AB:
    if b in tree[a]:
        continue
    answer.append('{} {}'.format(a,b))
    out_deg[a] += 1

def dfs(x = 1,parent = None):
    for y in tree[x]:
        if y == parent:
            continue
        dfs(y,x)
        if out_deg[y] & 1:
            answer.append('{} {}'.format(y,x))
            out_deg[y] += 1
        else:
            answer.append('{} {}'.format(x,y))
            out_deg[x] += 1

dfs()

print('\n'.join(answer))