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:
#editorial参照

import sys
from collections import deque
sys.setrecursionlimit(200000)

n,m = map(int, input().split( ))
G = [[] for _ in range(n)]

for _ in range(m):
    a,b = map(int, input().split( ))
    a-=1;b-=1
    G[a].append(b)
    G[b].append(a)

if m&1:
    print(-1)
    sys.exit()

Tr = [0]*n#k木に属しているか
Q = deque()
Q.append(0)
Tr[0] = 1
TrE = [[] for _ in range(n)]
P = [-1]*n#親
Leaf = []
while Q:
    v = Q.popleft()
    leaf_v = True
    for u in G[v]:
        if not Tr[u]:
            Tr[u] = 1
            P[u]=v
            TrE[v].append(u)
            Q.append(u)
            leaf_v = False
    if leaf_v:
        Leaf.append(v)

out = [0]*n
D = set()             
for v in range(n):
    for u in G[v]:
        if (u,v) not in D and P[v]!=u and P[u]!=v:
            D.add((v,u))
            out[v]^=1
            

"""
幅優先探索で葉から辿ったところ、
すべての子を考慮する前にpのdegreeが決まってしまっている。
深さ優先探索に修正
"""
def dfs(x = 0, parent = -1):
    for y in TrE[x]:
        if y == parent:
            continue
        dfs(y,x)
        if out[y]:
            D.add((y,x))
            out[y] ^= 1
        else:
            D.add((x,y))
            out[x] ^= 1
 
dfs()

for u,v in D:
    print(u+1,v+1)